|Part of a series on|
Dark matter is a hypothetical form of matter thought to account for approximately 85% of the matter in the universe. Dark matter is called "dark" because it does not appear to interact with the electromagnetic field, which means it does not absorb, reflect, or emit electromagnetic radiation (like light) and is, therefore, difficult to detect. Various astrophysical observations — including gravitational effects which cannot be explained by currently accepted theories of gravity unless more matter is present than can be seen — imply dark matter's presence. For this reason, most experts think that dark matter is abundant in the universe and has had a strong influence on its structure and evolution.
The primary evidence for dark matter comes from calculations showing that many galaxies would behave quite differently if they did not contain a large amount of unseen matter. Some galaxies would not have formed at all and others would not move as they currently do. Other lines of evidence include observations in gravitational lensing and the cosmic microwave background, along with astronomical observations of the observable universe's current structure, the formation and evolution of galaxies, mass location during galactic collisions, and the motion of galaxies within galaxy clusters. In the standard Lambda-CDM model of cosmology, the total mass-energy content of the universe contains 5% ordinary matter and energy, 27% dark matter, and 68% of a form of energy known as dark energy. Thus, dark matter constitutes 85%[lower-alpha 1] of the total mass, while dark energy and dark matter constitute 95% of the total mass-energy content.
Because no one has directly observed dark matter yet – assuming it exists – it must barely interact with ordinary baryonic matter and radiation except through gravity. Most dark matter is thought to be non-baryonic; it may be composed of some as-yet-undiscovered subatomic particles.[lower-alpha 2] The primary candidate for dark matter is some new kind of elementary particle that has not yet been discovered, particularly weakly interacting massive particles (WIMPs), though axions have drawn renewed attention due to the non-detection of WIMPs in experiments. Many experiments to directly detect and study dark matter particles are being actively undertaken, but none have yet succeeded. Dark matter is classified as "cold," "warm," or "hot" according to its velocity (more precisely, its free streaming length). Current models favor a cold dark matter scenario, in which structures emerge by the gradual accumulation of particles.
Although the scientific community generally accepts dark matter's existence, some astrophysicists, intrigued by specific observations that are not well-explained by ordinary dark matter, argue for various modifications of the standard laws of general relativity. These include modified Newtonian dynamics, tensor–vector–scalar gravity, or entropic gravity. These models attempt to account for all observations without invoking supplemental non-baryonic matter.
|Beyond the Standard Model|
The hypothesis of dark matter has an elaborate history. In a talk given in 1884, Lord Kelvin estimated the number of dark bodies in the Milky Way from the observed velocity dispersion of the stars orbiting around the center of the galaxy. By using these measurements, he estimated the mass of the galaxy, which he determined is different from the mass of visible stars. Lord Kelvin thus concluded "many of our stars, perhaps a great majority of them, may be dark bodies". In 1906, Henri Poincaré in "The Milky Way and Theory of Gases" used the French term matière obscure ("dark matter") in discussing Kelvin's work.
The first to suggest the existence of dark matter using stellar velocities was Dutch astronomer Jacobus Kapteyn in 1922. A publication from 1930 points to Swedish Knut Lundmark being the first to realise that the universe must contain much more mass than we can observe. Dutchman and radio astronomy pioneer Jan Oort also hypothesized the existence of dark matter in 1932. Oort was studying stellar motions in the local galactic neighborhood and found the mass in the galactic plane must be greater than what was observed, but this measurement was later determined to be erroneous.
In 1933, Swiss astrophysicist Fritz Zwicky, who studied galaxy clusters while working at the California Institute of Technology, made a similar inference. Zwicky applied the virial theorem to the Coma Cluster and obtained evidence of unseen mass he called dunkel Materie ('dark matter'). Zwicky estimated its mass based on the motions of galaxies near its edge and compared that to an estimate based on its brightness and number of galaxies. He estimated the cluster had about 400 times more mass than was visually observable. The gravity effect of the visible galaxies was far too small for such fast orbits, thus mass must be hidden from view. Based on these conclusions, Zwicky inferred some unseen matter provided the mass and associated gravitation attraction to hold the cluster together. Zwicky's estimates were off by more than an order of magnitude, mainly due to an obsolete value of the Hubble constant; the same calculation today shows a smaller fraction, using greater values for luminous mass. Nonetheless, Zwicky did correctly conclude from his calculation that the bulk of the matter was dark.
Further indications of mass-to-light ratio anomalies came from measurements of galaxy rotation curves. In 1939, Horace W. Babcock reported the rotation curve for the Andromeda nebula (known now as the Andromeda Galaxy), which suggested the mass-to-luminosity ratio increases radially. He attributed it to either light absorption within the galaxy or modified dynamics in the outer portions of the spiral and not to the missing matter he had uncovered. Following Babcock's 1939 report of unexpectedly rapid rotation in the outskirts of the Andromeda galaxy and a mass-to-light ratio of 50; in 1940 Jan Oort discovered and wrote about the large non-visible halo of NGC 3115.
Early radio astronomy observations, performed by Seth Shostak, later SETI Institute Senior Astronomer, showed a half-dozen galaxies spun too fast in their outer regions - pointing to the existence of dark matter. "Superstars of Astronomy podcast". https://astronomy.com/-/media/Files/PDF/Superstars/Shostak.pdf.
Vera Rubin, Kent Ford, and Ken Freeman's work in the 1960s and 1970s provided further strong evidence, also using galaxy rotation curves. Rubin and Ford worked with a new spectrograph to measure the velocity curve of edge-on spiral galaxies with greater accuracy. This result was confirmed in 1978. An influential paper presented Rubin and Ford's results in 1980. They showed most galaxies must contain about six times as much dark as visible mass; thus, by around 1980 the apparent need for dark matter was widely recognized as a major unsolved problem in astronomy.
At the same time Rubin and Ford were exploring optical rotation curves, radio astronomers were making use of new radio telescopes to map the 21 cm line of atomic hydrogen in nearby galaxies. The radial distribution of interstellar atomic hydrogen (H-I) often extends to much larger galactic radii than those accessible by optical studies, extending the sampling of rotation curves – and thus of the total mass distribution – to a new dynamical regime. Early mapping of Andromeda with the 300 foot telescope at Green Bank and the 250 foot dish at Jodrell Bank already showed the H-I rotation curve did not trace the expected Keplerian decline. As more sensitive receivers became available, Morton Roberts and Robert Whitehurst were able to trace the rotational velocity of Andromeda to 30 kpc, much beyond the optical measurements. Illustrating the advantage of tracing the gas disk at large radii, Figure 16 of that paper combines the optical data (the cluster of points at radii of less than 15 kpc with a single point further out) with the H-I data between 20–30 kpc, exhibiting the flatness of the outer galaxy rotation curve; the solid curve peaking at the center is the optical surface density, while the other curve shows the cumulative mass, still rising linearly at the outermost measurement. In parallel, the use of interferometric arrays for extragalactic H-I spectroscopy was being developed. In 1972, David Rogstad and Seth Shostak published H-I rotation curves of five spirals mapped with the Owens Valley interferometer; the rotation curves of all five were very flat, suggesting very large values of mass-to-light ratio in the outer parts of their extended H-I disks.
A stream of observations in the 1980s supported the presence of dark matter, including gravitational lensing of background objects by galaxy clusters, the temperature distribution of hot gas in galaxies and clusters, and the pattern of anisotropies in the cosmic microwave background. According to consensus among cosmologists, dark matter is composed primarily of a not yet characterized type of subatomic particle. The search for this particle, by a variety of means, is one of the major efforts in particle physics.
In standard cosmology, matter is anything whose energy density scales with the inverse cube of the scale factor, i.e., ρ ∝ a−3. This is in contrast to radiation, which scales as the inverse fourth power of the scale factor ρ ∝ a−4, and a cosmological constant, which is independent of a. These scalings can be understood intuitively: For an ordinary particle in a cubical box, doubling the length of the sides of the box decreases the density (and hence energy density) by a factor of 8 (= 23). For radiation, the energy density decreases by a factor of 16 (= 24), because any act whose effect increases the scale factor must also cause a proportional redshift. A cosmological constant, as an intrinsic property of space, has a constant energy density regardless of the volume under consideration.[lower-alpha 3]
In principle, "dark matter" means all components of the universe which are not visible but still obey ρ ∝ a−3. In practice, the term "dark matter" is often used to mean only the non-baryonic component of dark matter, i.e., excluding "missing baryons". Context will usually indicate which meaning is intended.
Galaxy rotation curves
The arms of spiral galaxies rotate around the galactic center. The luminous mass density of a spiral galaxy decreases as one goes from the center to the outskirts. If luminous mass were all the matter, then we can model the galaxy as a point mass in the centre and test masses orbiting around it, similar to the Solar System.[lower-alpha 4] From Kepler's Second Law, it is expected that the rotation velocities will decrease with distance from the center, similar to the Solar System. This is not observed. Instead, the galaxy rotation curve remains flat as distance from the center increases.
If Kepler's laws are correct, then the obvious way to resolve this discrepancy is to conclude the mass distribution in spiral galaxies is not similar to that of the Solar System. In particular, there is a lot of non-luminous matter (dark matter) in the outskirts of the galaxy.
Stars in bound systems must obey the virial theorem. The theorem, together with the measured velocity distribution, can be used to measure the mass distribution in a bound system, such as elliptical galaxies or globular clusters. With some exceptions, velocity dispersion estimates of elliptical galaxies do not match the predicted velocity dispersion from the observed mass distribution, even assuming complicated distributions of stellar orbits.
As with galaxy rotation curves, the obvious way to resolve the discrepancy is to postulate the existence of non-luminous matter.
Galaxy clusters are particularly important for dark matter studies since their masses can be estimated in three independent ways:
- From the scatter in radial velocities of the galaxies within clusters
- From X-rays emitted by hot gas in the clusters. From the X-ray energy spectrum and flux, the gas temperature and density can be estimated, hence giving the pressure; assuming pressure and gravity balance determines the cluster's mass profile.
- Gravitational lensing (usually of more distant galaxies) can measure cluster masses without relying on observations of dynamics (e.g., velocity).
Generally, these three methods are in reasonable agreement that dark matter outweighs visible matter by approximately 5 to 1.
One of the consequences of general relativity is massive objects (such as a cluster of galaxies) lying between a more distant source (such as a quasar) and an observer should act as a lens to bend the light from this source. The more massive an object, the more lensing is observed.
Strong lensing is the observed distortion of background galaxies into arcs when their light passes through such a gravitational lens. It has been observed around many distant clusters including Abell 1689. By measuring the distortion geometry, the mass of the intervening cluster can be obtained. In the dozens of cases where this has been done, the mass-to-light ratios obtained correspond to the dynamical dark matter measurements of clusters. Lensing can lead to multiple copies of an image. By analyzing the distribution of multiple image copies, scientists have been able to deduce and map the distribution of dark matter around the MACS J0416.1-2403 galaxy cluster.
Weak gravitational lensing investigates minute distortions of galaxies, using statistical analyses from vast galaxy surveys. By examining the apparent shear deformation of the adjacent background galaxies, the mean distribution of dark matter can be characterized. The mass-to-light ratios correspond to dark matter densities predicted by other large-scale structure measurements. Dark matter does not bend light itself; mass (in this case the mass of the dark matter) bends spacetime. Light follows the curvature of spacetime, resulting in the lensing effect.
In May 2021, a new detailed dark matter map was revealed by the Dark Energy Survey Collaboration. In addition, the map revealed previously undiscovered filamentary structures connecting galaxies, by using a machine learning method.
Cosmic microwave background
Although both dark matter and ordinary matter are matter, they do not behave in the same way. In particular, in the early universe, ordinary matter was ionized and interacted strongly with radiation via Thomson scattering. Dark matter does not interact directly with radiation, but it does affect the cosmic microwave background (CMB) by its gravitational potential (mainly on large scales) and by its effects on the density and velocity of ordinary matter. Ordinary and dark matter perturbations, therefore, evolve differently with time and leave different imprints on the CMB.
The cosmic microwave background is very close to a perfect blackbody but contains very small temperature anisotropies of a few parts in 100,000. A sky map of anisotropies can be decomposed into an angular power spectrum, which is observed to contain a series of acoustic peaks at near-equal spacing but different heights. The series of peaks can be predicted for any assumed set of cosmological parameters by modern computer codes such as CMBFAST and CAMB, and matching theory to data, therefore, constrains cosmological parameters. The first peak mostly shows the density of baryonic matter, while the third peak relates mostly to the density of dark matter, measuring the density of matter and the density of atoms.
The CMB anisotropy was first discovered by COBE in 1992, though this had too coarse resolution to detect the acoustic peaks. After the discovery of the first acoustic peak by the balloon-borne BOOMERanG experiment in 2000, the power spectrum was precisely observed by WMAP in 2003–2012, and even more precisely by the Planck spacecraft in 2013–2015. The results support the Lambda-CDM model.
The observed CMB angular power spectrum provides powerful evidence in support of dark matter, as its precise structure is well fitted by the Lambda-CDM model, but difficult to reproduce with any competing model such as modified Newtonian dynamics (MOND).
Structure formation refers to the period after the Big Bang when density perturbations collapsed to form stars, galaxies, and clusters. Prior to structure formation, the Friedmann solutions to general relativity describe a homogeneous universe. Later, small anisotropies gradually grew and condensed the homogeneous universe into stars, galaxies and larger structures. Ordinary matter is affected by radiation, which is the dominant element of the universe at very early times. As a result, its density perturbations are washed out and unable to condense into structure. If there were only ordinary matter in the universe, there would not have been enough time for density perturbations to grow into the galaxies and clusters currently seen.
Dark matter provides a solution to this problem because it is unaffected by radiation. Therefore, its density perturbations can grow first. The resulting gravitational potential acts as an attractive potential well for ordinary matter collapsing later, speeding up the structure formation process.
If dark matter does not exist, then the next most likely explanation must be that general relativity – the prevailing theory of gravity – is incorrect and should be modified. The Bullet Cluster, the result of a recent collision of two galaxy clusters, provides a challenge for modified gravity theories because its apparent center of mass is far displaced from the baryonic center of mass. Standard dark matter models can easily explain this observation, but modified gravity has a much harder time, especially since the observational evidence is model-independent.
Type Ia supernova distance measurements
Type Ia supernovae can be used as standard candles to measure extragalactic distances, which can in turn be used to measure how fast the universe has expanded in the past. Data indicates the universe is expanding at an accelerating rate, the cause of which is usually ascribed to dark energy. Since observations indicate the universe is almost flat, it is expected the total energy density of everything in the universe should sum to 1 (Ωtot ≈ 1). The measured dark energy density is ΩΛ ≈ 0.690; the observed ordinary (baryonic) matter energy density is Ωb ≈ 0.0482 and the energy density of radiation is negligible. This leaves a missing Ωdm ≈ 0.258 which nonetheless behaves like matter (see technical definition section above) – dark matter.
Sky surveys and baryon acoustic oscillations
Baryon acoustic oscillations (BAO) are fluctuations in the density of the visible baryonic matter (normal matter) of the universe on large scales. These are predicted to arise in the Lambda-CDM model due to acoustic oscillations in the photon–baryon fluid of the early universe, and can be observed in the cosmic microwave background angular power spectrum. BAOs set up a preferred length scale for baryons. As the dark matter and baryons clumped together after recombination, the effect is much weaker in the galaxy distribution in the nearby universe, but is detectable as a subtle (≈1 percent) preference for pairs of galaxies to be separated by 147 Mpc, compared to those separated by 130–160 Mpc. This feature was predicted theoretically in the 1990s and then discovered in 2005, in two large galaxy redshift surveys, the Sloan Digital Sky Survey and the 2dF Galaxy Redshift Survey. Combining the CMB observations with BAO measurements from galaxy redshift surveys provides a precise estimate of the Hubble constant and the average matter density in the Universe. The results support the Lambda-CDM model.
Large galaxy redshift surveys may be used to make a three-dimensional map of the galaxy distribution. These maps are slightly distorted because distances are estimated from observed redshifts; the redshift contains a contribution from the galaxy's so-called peculiar velocity in addition to the dominant Hubble expansion term. On average, superclusters are expanding more slowly than the cosmic mean due to their gravity, while voids are expanding faster than average. In a redshift map, galaxies in front of a supercluster have excess radial velocities towards it and have redshifts slightly higher than their distance would imply, while galaxies behind the supercluster have redshifts slightly low for their distance. This effect causes superclusters to appear squashed in the radial direction, and likewise voids are stretched. Their angular positions are unaffected. This effect is not detectable for any one structure since the true shape is not known, but can be measured by averaging over many structures. It was predicted quantitatively by Nick Kaiser in 1987, and first decisively measured in 2001 by the 2dF Galaxy Redshift Survey. Results are in agreement with the Lambda-CDM model.
In astronomical spectroscopy, the Lyman-alpha forest is the sum of the absorption lines arising from the Lyman-alpha transition of neutral hydrogen in the spectra of distant galaxies and quasars. Lyman-alpha forest observations can also constrain cosmological models. These constraints agree with those obtained from WMAP data.
There are various hypotheses about what dark matter could consist of, as set out in the table below.
|Unsolved problem in physics:|
What is dark matter? How was it generated?(more unsolved problems in physics)
|Light bosons||quantum chromodynamics axions|
|fuzzy cold dark matter|
|effective field theory|
|other particles||Weakly interacting massive particles|
|self-interacting dark matter|
|superfluid vacuum theory|
|macroscopic||primordial black holes|
|massive compact halo objects (MaCHOs)|
|Macroscopic dark matter (Macros)|
|modified gravity (MOG)||modified Newtonian dynamics (MoND)|
|Tensor–vector–scalar gravity (TeVeS)|
Dark matter can refer to any substance which interacts predominantly via gravity with visible matter (e.g., stars and planets). Hence in principle it need not be composed of a new type of fundamental particle but could, at least in part, be made up of standard baryonic matter, such as protons or neutrons.[lower-alpha 5] However, for the reasons outlined below, most scientists think the dark matter is dominated by a non-baryonic component, which is likely composed of a currently unknown fundamental particle (or similar exotic state).
Baryons (protons and neutrons) make up ordinary stars and planets. However, baryonic matter also encompasses less common non-primordial black holes, neutron stars, faint old white dwarfs and brown dwarfs, collectively known as massive compact halo objects (MACHOs), which can be hard to detect.
However, multiple lines of evidence suggest the majority of dark matter is not made of baryons:
- Sufficient diffuse, baryonic gas or dust would be visible when backlit by stars.
- The theory of Big Bang nucleosynthesis predicts the observed abundance of the chemical elements. If there are more baryons, then there should also be more helium, lithium and heavier elements synthesized during the Big Bang. Agreement with observed abundances requires that baryonic matter makes up between 4–5% of the universe's critical density. In contrast, large-scale structure and other observations indicate that the total matter density is about 30% of the critical density.
- Astronomical searches for gravitational microlensing in the Milky Way found at most only a small fraction of the dark matter may be in dark, compact, conventional objects (MACHOs, etc.); the excluded range of object masses is from half the Earth's mass up to 30 solar masses, which covers nearly all the plausible candidates.
- Detailed analysis of the small irregularities (anisotropies) in the cosmic microwave background. Observations by WMAP and Planck indicate that around five-sixths of the total matter is in a form that interacts significantly with ordinary matter or photons only through gravitational effects.
Candidates for non-baryonic dark matter are hypothetical particles such as axions, sterile neutrinos, weakly interacting massive particles (WIMPs), supersymmetric particles, geons, or primordial black holes. The three neutrino types already observed are indeed abundant, and dark, and matter, but because their individual masses – however uncertain they may be – are almost certainly too tiny, they can only supply a small fraction of dark matter, due to limits derived from large-scale structure and high-redshift galaxies.
Unlike baryonic matter, nonbaryonic matter did not contribute to the formation of the elements in the early universe (Big Bang nucleosynthesis) and so its presence is revealed only via its gravitational effects, or weak lensing. In addition, if the particles of which it is composed are supersymmetric, they can undergo annihilation interactions with themselves, possibly resulting in observable by-products such as gamma rays and neutrinos (indirect detection).
Dark matter aggregation and dense dark matter objects
If dark matter is composed of weakly-interacting particles, then an obvious question is whether it can form objects equivalent to planets, stars, or black holes. Historically, the answer has been it cannot, because of two factors:
- It lacks an efficient means to lose energy
- Ordinary matter forms dense objects because it has numerous ways to lose energy. Losing energy would be essential for object formation, because a particle that gains energy during compaction or falling "inward" under gravity, and cannot lose it any other way, will heat up and increase velocity and momentum. Dark matter appears to lack a means to lose energy, simply because it is not capable of interacting strongly in other ways except through gravity. The virial theorem suggests that such a particle would not stay bound to the gradually forming object – as the object began to form and compact, the dark matter particles within it would speed up and tend to escape.
- It lacks a range of interactions needed to form structures
- Ordinary matter interacts in many different ways, which allows the matter to form more complex structures. For example, stars form through gravity, but the particles within them interact and can emit energy in the form of neutrinos and electromagnetic radiation through fusion when they become energetic enough. Protons and neutrons can bind via the strong interaction and then form atoms with electrons largely through electromagnetic interaction. There is no evidence that dark matter is capable of such a wide variety of interactions, since it seems to only interact through gravity (and possibly through some means no stronger than the weak interaction, although until dark matter is better understood, this is only speculation).
In 2015–2017, the idea that dense dark matter was composed of primordial black holes made a comeback following results of gravitational wave measurements which detected the merger of intermediate-mass black holes. Black holes with about 30 solar masses are not predicted to form by either stellar collapse (typically less than 15 solar masses) or by the merger of black holes in galactic centers (millions or billions of solar masses). It was proposed that the intermediate-mass black holes causing the detected merger formed in the hot dense early phase of the universe due to denser regions collapsing. A later survey of about a thousand supernovae detected no gravitational lensing events, when about eight would be expected if intermediate-mass primordial black holes above a certain mass range accounted for the majority of dark matter.
The possibility that atom-sized primordial black holes account for a significant fraction of dark matter was ruled out by measurements of positron and electron fluxes outside the Sun's heliosphere by the Voyager 1 spacecraft. Tiny black holes are theorized to emit Hawking radiation. However the detected fluxes were too low and did not have the expected energy spectrum, suggesting that tiny primordial black holes are not widespread enough to account for dark matter. Nonetheless, research and theories proposing dense dark matter accounts for dark matter continue as of 2018, including approaches to dark matter cooling, and the question remains unsettled. In 2019, the lack of microlensing effects in the observation of Andromeda suggests that tiny black holes do not exist.
However, there still exists a largely unconstrained mass range smaller than that which can be limited by optical microlensing observations, where primordial black holes may account for all dark matter.
Free streaming length
Dark matter can be divided into cold, warm, and hot categories. These categories refer to velocity rather than an actual temperature, indicating how far corresponding objects moved due to random motions in the early universe, before they slowed due to cosmic expansion – this is an important distance called the free streaming length (FSL). Primordial density fluctuations smaller than this length get washed out as particles spread from overdense to underdense regions, while larger fluctuations are unaffected; therefore this length sets a minimum scale for later structure formation.
The categories are set with respect to the size of a protogalaxy (an object that later evolves into a dwarf galaxy): Dark matter particles are classified as cold, warm, or hot according to their FSL; much smaller (cold), similar to (warm), or much larger (hot) than a protogalaxy. Mixtures of the above are also possible: a theory of mixed dark matter was popular in the mid-1990s, but was rejected following the discovery of dark energy.
Cold dark matter leads to a bottom-up formation of structure with galaxies forming first and galaxy clusters at a latter stage, while hot dark matter would result in a top-down formation scenario with large matter aggregations forming early, later fragmenting into separate galaxies;[clarification needed] the latter is excluded by high-redshift galaxy observations.
Fluctuation spectrum effects
Candidate particles can be grouped into three categories on the basis of their effect on the fluctuation spectrum (Bond et al. 1983). If the dark matter is composed of abundant light particles which remain relativistic until shortly before recombination, then it may be termed "hot". The best candidate for hot dark matter is a neutrino ... A second possibility is for the dark matter particles to interact more weakly than neutrinos, to be less abundant, and to have a mass of order 1 keV. Such particles are termed "warm dark matter", because they have lower thermal velocities than massive neutrinos ... there are at present few candidate particles which fit this description. Gravitinos and photinos have been suggested (Pagels and Primack 1982; Bond, Szalay and Turner 1982) ... Any particles which became nonrelativistic very early, and so were able to diffuse a negligible distance, are termed "cold" dark matter (CDM). There are many candidates for CDM including supersymmetric particles.—M. Davis, G. Efstathiou, C.S. Frenk, and S.D.M. White , The evolution of large-scale structure in a universe dominated by cold dark matter
Another approximate dividing line is warm dark matter became non-relativistic when the universe was approximately 1 year old and 1 millionth of its present size and in the radiation-dominated era (photons and neutrinos), with a photon temperature 2.7 million Kelvins. Standard physical cosmology gives the particle horizon size as 2 c t (speed of light multiplied by time) in the radiation-dominated era, thus 2 light-years. A region of this size would expand to 2 million light-years today (absent structure formation). The actual FSL is approximately 5 times the above length, since it continues to grow slowly as particle velocities decrease inversely with the scale factor after they become non-relativistic. In this example the FSL would correspond to 10 million light-years, or 3 megaparsecs, today, around the size containing an average large galaxy.
The 2.7 million K photon temperature gives a typical photon energy of 250 electronvolts, thereby setting a typical mass scale for warm dark matter: particles much more massive than this, such as GeV–TeV mass WIMPs, would become non-relativistic much earlier than one year after the Big Bang and thus have FSLs much smaller than a protogalaxy, making them cold. Conversely, much lighter particles, such as neutrinos with masses of only a few eV, have FSLs much larger than a protogalaxy, thus qualifying them as hot.
Cold dark matter
Cold dark matter offers the simplest explanation for most cosmological observations. It is dark matter composed of constituents with an FSL much smaller than a protogalaxy. This is the focus for dark matter research, as hot dark matter does not seem capable of supporting galaxy or galaxy cluster formation, and most particle candidates slowed early.
The constituents of cold dark matter are unknown. Possibilities range from large objects like MACHOs (such as black holes and Preon stars) or RAMBOs (such as clusters of brown dwarfs), to new particles such as WIMPs and axions.
Studies of Big Bang nucleosynthesis and gravitational lensing convinced most cosmologists that MACHOs cannot make up more than a small fraction of dark matter. According to A. Peter: "... the only really plausible dark-matter candidates are new particles."
The 1997 DAMA/NaI experiment and its successor DAMA/LIBRA in 2013, claimed to directly detect dark matter particles passing through the Earth, but many researchers remain skeptical, as negative results from similar experiments seem incompatible with the DAMA results.
Many supersymmetric models offer dark matter candidates in the form of the WIMPy Lightest Supersymmetric Particle (LSP). Separately, heavy sterile neutrinos exist in non-supersymmetric extensions to the standard model which explain the small neutrino mass through the seesaw mechanism.
Warm dark matter
Warm dark matter comprises particles with an FSL comparable to the size of a protogalaxy. Predictions based on warm dark matter are similar to those for cold dark matter on large scales, but with less small-scale density perturbations. This reduces the predicted abundance of dwarf galaxies and may lead to lower density of dark matter in the central parts of large galaxies. Some researchers consider this a better fit to observations. A challenge for this model is the lack of particle candidates with the required mass ≈ 300 eV to 3000 eV.
No known particles can be categorized as warm dark matter. A postulated candidate is the sterile neutrino: A heavier, slower form of neutrino that does not interact through the weak force, unlike other neutrinos. Some modified gravity theories, such as scalar–tensor–vector gravity, require "warm" dark matter to make their equations work.
Hot dark matter
Hot dark matter consists of particles whose FSL is much larger than the size of a protogalaxy. The neutrino qualifies as such particle. They were discovered independently, long before the hunt for dark matter: they were postulated in 1930, and detected in 1956. Neutrinos' mass is less than 10−6 that of an electron. Neutrinos interact with normal matter only via gravity and the weak force, making them difficult to detect (the weak force only works over a small distance, thus a neutrino triggers a weak force event only if it hits a nucleus head-on). This makes them “weakly interacting slender particles” (WISPs), as opposed to WIMPs.
The three known flavours of neutrinos are the electron, muon, and tau. Their masses are slightly different. Neutrinos oscillate among the flavours as they move. It is hard to determine an exact upper bound on the collective average mass of the three neutrinos (or for any of the three individually). For example, if the average neutrino mass were over 50 eV/c2 (less than 10−5 of the mass of an electron), the universe would collapse. CMB data and other methods indicate that their average mass probably does not exceed 0.3 eV/c2. Thus, observed neutrinos cannot explain dark matter.
Because galaxy-size density fluctuations get washed out by free-streaming, hot dark matter implies the first objects that can form are huge supercluster-size pancakes, which then fragment into galaxies. Deep-field observations show instead that galaxies formed first, followed by clusters and superclusters as galaxies clump together.
Detection of dark matter particles
If dark matter is made up of subatomic particles, then millions, possibly billions, of such particles must pass through every square centimeter of the Earth each second. Many experiments aim to test this hypothesis. Although WIMPs have been the main search candidates, axions have drawn renewed attention, with the Axion Dark Matter Experiment (ADMX) searches for axions and many more planned in the future. Another candidate is heavy hidden sector particles which only interact with ordinary matter via gravity.
These experiments can be divided into two classes: direct detection experiments, which search for the scattering of dark matter particles off atomic nuclei within a detector; and indirect detection, which look for the products of dark matter particle annihilations or decays.
Direct detection experiments aim to observe low-energy recoils (typically a few keVs) of nuclei induced by interactions with particles of dark matter, which (in theory) are passing through the Earth. After such a recoil the nucleus will emit energy in the form of scintillation light or phonons, as they pass through sensitive detection apparatus. To do so effectively, it is crucial to maintain an extremely low background, which is the reason why such experiments typically operate deep underground, where interference from cosmic rays is minimized. Examples of underground laboratories with direct detection experiments include the Stawell mine, the Soudan mine, the SNOLAB underground laboratory at Sudbury, the Gran Sasso National Laboratory, the Canfranc Underground Laboratory, the Boulby Underground Laboratory, the Deep Underground Science and Engineering Laboratory and the China Jinping Underground Laboratory.
These experiments mostly use either cryogenic or noble liquid detector technologies. Cryogenic detectors operating at temperatures below 100 mK, detect the heat produced when a particle hits an atom in a crystal absorber such as germanium. Noble liquid detectors detect scintillation produced by a particle collision in liquid xenon or argon. Cryogenic detector experiments include: CDMS, CRESST, EDELWEISS, EURECA. Noble liquid experiments include LZ, XENON, DEAP, ArDM, WARP, DarkSide, PandaX, and LUX, the Large Underground Xenon experiment. Both of these techniques focus strongly on their ability to distinguish background particles (which predominantly scatter off electrons) from dark matter particles (that scatter off nuclei). Other experiments include SIMPLE and PICASSO.
Currently there has been no well-established claim of dark matter detection from a direct detection experiment, leading instead to strong upper limits on the mass and interaction cross section with nucleons of such dark matter particles. The DAMA/NaI and more recent DAMA/LIBRA experimental collaborations have detected an annual modulation in the rate of events in their detectors, which they claim is due to dark matter. This results from the expectation that as the Earth orbits the Sun, the velocity of the detector relative to the dark matter halo will vary by a small amount. This claim is so far unconfirmed and in contradiction with negative results from other experiments such as LUX, SuperCDMS and XENON100.
A special case of direct detection experiments covers those with directional sensitivity. This is a search strategy based on the motion of the Solar System around the Galactic Center. A low-pressure time projection chamber makes it possible to access information on recoiling tracks and constrain WIMP-nucleus kinematics. WIMPs coming from the direction in which the Sun travels (approximately towards Cygnus) may then be separated from background, which should be isotropic. Directional dark matter experiments include DMTPC, DRIFT, Newage and MIMAC.
File:Turning Black Holes into Dark Matter Labs.webm Indirect detection experiments search for the products of the self-annihilation or decay of dark matter particles in outer space. For example, in regions of high dark matter density (e.g., the centre of our galaxy) two dark matter particles could annihilate to produce gamma rays or Standard Model particle–antiparticle pairs. Alternatively, if a dark matter particle is unstable, it could decay into Standard Model (or other) particles. These processes could be detected indirectly through an excess of gamma rays, antiprotons or positrons emanating from high density regions in our galaxy or others. A major difficulty inherent in such searches is that various astrophysical sources can mimic the signal expected from dark matter, and so multiple signals are likely required for a conclusive discovery.
A few of the dark matter particles passing through the Sun or Earth may scatter off atoms and lose energy. Thus dark matter may accumulate at the center of these bodies, increasing the chance of collision/annihilation. This could produce a distinctive signal in the form of high-energy neutrinos. Such a signal would be strong indirect proof of WIMP dark matter. High-energy neutrino telescopes such as AMANDA, IceCube and ANTARES are searching for this signal. The detection by LIGO in September 2015 of gravitational waves opens the possibility of observing dark matter in a new way, particularly if it is in the form of primordial black holes.
Many experimental searches have been undertaken to look for such emission from dark matter annihilation or decay, examples of which follow. The Energetic Gamma Ray Experiment Telescope observed more gamma rays in 2008 than expected from the Milky Way, but scientists concluded this was most likely due to incorrect estimation of the telescope's sensitivity.
The Fermi Gamma-ray Space Telescope is searching for similar gamma rays. In April 2012, an analysis of previously available data from its Large Area Telescope instrument produced statistical evidence of a 130 GeV signal in the gamma radiation coming from the center of the Milky Way. WIMP annihilation was seen as the most probable explanation.
In 2013 results from the Alpha Magnetic Spectrometer on the International Space Station indicated excess high-energy cosmic rays which could be due to dark matter annihilation.
Collider searches for dark matter
An alternative approach to the detection of dark matter particles in nature is to produce them in a laboratory. Experiments with the Large Hadron Collider (LHC) may be able to detect dark matter particles produced in collisions of the LHC proton beams. Because a dark matter particle should have negligible interactions with normal visible matter, it may be detected indirectly as (large amounts of) missing energy and momentum that escape the detectors, provided other (non-negligible) collision products are detected. Constraints on dark matter also exist from the LEP experiment using a similar principle, but probing the interaction of dark matter particles with electrons rather than quarks. Any discovery from collider searches must be corroborated by discoveries in the indirect or direct detection sectors to prove that the particle discovered is, in fact, dark matter.
Because dark matter has not yet been identified, many other hypotheses have emerged aiming to explain the observational phenomena that dark matter was conceived to explain. The most common method is to modify general relativity. General relativity is well-tested on solar system scales, but its validity on galactic or cosmological scales has not been well proven. A suitable modification to general relativity can in principle conceivably eliminate the need for dark matter. The best-known theories of this class are MOND and its relativistic generalization tensor-vector-scalar gravity (TeVeS), f(R) gravity, negative mass, dark fluid, and entropic gravity. Alternative theories abound.
A problem with alternative hypotheses is that observational evidence for dark matter comes from so many independent approaches (see the "observational evidence" section above). Explaining any individual observation is possible but explaining all of them in the absence of dark matter is very difficult. Nonetheless, there have been some scattered successes for alternative hypotheses, such as a 2016 test of gravitational lensing in entropic gravity and a 2020 measurement of a unique MOND effect.
The prevailing opinion among most astrophysicists is that while modifications to general relativity can conceivably explain part of the observational evidence, there is probably enough data to conclude there must be some form of dark matter present in the Universe.
In popular culture
Mention of dark matter is made in works of fiction. In such cases, it is usually attributed extraordinary physical or magical properties. Such descriptions are often inconsistent with the hypothesized properties of dark matter in physics and cosmology.
- Related theories
- Astronomy:Dark energy – Unknown property in cosmology that causes the expansion of the universe to accelerate.
- Physics:Conformal gravity – Gravity theories that are invariant under Weyl transformations
- Density wave theory – A theory in which waves of compressed gas, which move slower than the galaxy, maintain galaxy's structure
- Physics:Entropic gravity – Theory in modern physics that describes gravity as an entropic force
- Astronomy:Dark radiation – Postulated type of radiation that mediates interactions of dark matter
- Physics:Massive gravity – Theory of gravity in which the graviton has nonzero mass
- Physics:Unparticle physics – Speculative theory that conjectures a form of matter that cannot be explained in terms of particles
- Physics:DEAP, a search apparatus
- Earth:LZ experiment, large underground dark matter detector
- Astronomy:Dark Matter Particle Explorer (DAMPE), a space mission
- Physics:General antiparticle spectrometer
- Physics:MultiDark, a research program
- Astronomy:Illustris project – Computer-simulated universes, astrophysical simulations
- Physics:Future Circular Collider – Proposed post-LHC particle accelerator at CERN, Geneva, Switzerland, a particle accelerator research infrastructure
- Dark matter candidates
- Physics:Light dark matter – Dark matter weakly interacting massive particles candidates with masses less than 1 GeV
- Physics:Mirror matter – Hypothetical counterpart to ordinary matter
- Physics:Exotic matter – Any kind of non-baryonic matter
- Astronomy:Dark galaxy – A hypothesized galaxy with no, or very few, stars
- Physics:Scalar field dark matter – Classical, minimally coupled, scalar field postulated to account for the inferred dark matter
- Astronomy:Self-interacting dark matter – Hypothetical form of dark matter consisting of particles with strong self-interactions
- Physics:Weakly interacting massive particles (WIMP) – Hypothetical particles that are thought to constitute dark matter
- Weakly interacting slim particle (WISP) — Low-mass counterpart to WIMP
- Astronomy:Strongly interacting massive particle (SIMP) – Hypothetical particles that interact strongly with ordinary matter, but could form the inferred dark matter despite this
- Physics:Chameleon particle – Hypothetical scalar particle that couples to matter more weakly than gravity
- Astronomy:Galactic Center GeV excess – Unexplained gamma-ray radiation in center of Milky Way galaxy
- Since dark energy does not count as matter, this is 26.8/ = 0.845
- A small portion of dark matter could be baryonic and/or neutrinos. See Baryonic dark matter.
- Dark energy is a term often used nowadays as a substitute for cosmological constant. It is basically the same except that dark energy might depend on scale factor in some unknown way rather than necessarily being constant.
- This is a consequence of the shell theorem and the observation that spiral galaxies are spherically symmetric to a large extent (in 2D).
- Astronomers define the term baryonic matter to refer to ordinary matter made of protons, neutrons and electrons, including neutron stars and black holes from the collapse of ordinary matter. Strictly speaking, electrons are leptons not baryons; but since their number is equal to the protons while their mass is far smaller, electrons give a negligible contribution to the average density of baryonic matter. Baryonic matter excludes other known particles such as photons and neutrinos. Hypothetical primordial black holes are also generally defined as non-baryonic, since they would have formed from radiation, not matter.
- "NASA Science Universe – Dark Energy, Dark Matter". https://science.nasa.gov/astrophysics/focus-areas/what-is-dark-energy.
- "Dark Matter". 20 January 2012. http://home.cern/about/physics/dark-matter.
- Siegfried, T. (5 July 1999). "Hidden space dimensions may permit parallel universes, explain cosmic mysteries". The Dallas Morning News. http://www.physics.ucdavis.edu/~kaloper/siegfr.txt.
- Trimble, V. (1987). "Existence and nature of dark matter in the universe". Annual Review of Astronomy and Astrophysics 25: 425–472. doi:10.1146/annurev.aa.25.090187.002233. Bibcode: 1987ARA&A..25..425T. https://cloudfront.escholarship.org/dist/prd/content/qt2hz008rs/qt2hz008rs.pdf.
- "A history of dark matter". 2017. https://arstechnica.com/science/2017/02/a-history-of-dark-matter.
- "Planck Mission Brings Universe into Sharp Focus". 21 March 2013. http://www.nasa.gov/mission_pages/planck/news/planck20130321.html.
- "Dark Energy, Dark Matter". 5 June 2015. https://science.nasa.gov/astrophysics/focus-areas/what-is-dark-energy/.
- Ade, P.A.R. et al. (22 March 2013). "Planck 2013 results. I. Overview of products and scientific results – Table 9". Astronomy and Astrophysics 1303: 5062. doi:10.1051/0004-6361/201321529. Bibcode: 2014A&A...571A...1P. http://www.cosmos.esa.int/web/planck/publications.
- Francis, Matthew (22 March 2013). "First Planck results: the Universe is still weird and interesting". https://arstechnica.com/science/2013/03/first-planck-results-the-universe-is-still-weird-and-interesting/.
- "Planck captures portrait of the young Universe, revealing earliest light". University of Cambridge. 21 March 2013. http://www.cam.ac.uk/research/news/planck-captures-portrait-of-the-young-universe-revealing-earliest-light.
- Carroll, Sean (2007). Dark Matter, Dark Energy: The dark side of the universe. The Teaching Company. Guidebook Part 2 p. 46. "... dark matter: An invisible, essentially collisionless component of matter that makes up about 25 percent of the energy density of the universe ... it's a different kind of particle... something not yet observed in the laboratory ..."
- Ferris, Timothy (January 2015). "Dark matter". National Geographic Magazine. http://ngm.nationalgeographic.com/2015/01/hidden-cosmos/ferris-text. Retrieved 10 June 2015.
- Jarosik, N. (2011). "Seven-year Wilson microwave anisotropy probe (WMAP) observations: Sky maps, systematic errors, and basic results". Astrophysical Journal Supplement 192 (2): 14. doi:10.1088/0067-0049/192/2/14. Bibcode: 2011ApJS..192...14J.
- Copi, C.J.; Schramm, D.N.; Turner, M.S. (1995). "Big-Bang Nucleosynthesis and the Baryon Density of the Universe". Science 267 (5195): 192–199. doi:10.1126/science.7809624. PMID 7809624. Bibcode: 1995Sci...267..192C. http://cds.cern.ch/record/265576.
- Francesca Chadha-Day; John Ellis; David J. E. Marsh (23 February 2022). "Axion dark matter: What is it and why now?". Science Advances 8 (8). doi:10.1126/sciadv.abj3618. https://www.science.org/doi/10.1126/sciadv.abj3618. Retrieved 25 March 2022.
- Bertone, G.; Hooper, D.; Silk, J. (2005). "Particle dark matter: Evidence, candidates and constraints". Physics Reports 405 (5–6): 279–390. doi:10.1016/j.physrep.2004.08.031. Bibcode: 2005PhR...405..279B.
- Hossenfelder, Sabine and McGaugh, Stacy S (August 2018). "Is dark matter real?". Scientific American 319 (2): 36–43. doi:10.1038/scientificamerican0818-36. PMID 30020902. Bibcode: 2018SciAm.319b..36H. https://www.scientificamerican.com/article/is-dark-matter-real/. "Right now a few dozens of scientists are studying modified gravity, whereas several thousand are looking for particle dark matter."
- de Swart, J.G.; Bertone, G.; van Dongen, J. (2017). "How dark matter came to matter". Nature Astronomy 1 (59): 0059. doi:10.1038/s41550-017-0059. Bibcode: 2017NatAs...1E..59D.
- "A History of Dark Matter- Gianfranco Bertone & Dan Hooper". https://ned.ipac.caltech.edu/level5/Sept16/Bertone/Bertone2.html.
- Kelvin, Lord (1904). Baltimore Lectures on Molecular Dynamics and the Wave Theory of Light. London, England: C.J. Clay and Sons. p. 274. https://babel.hathitrust.org/cgi/pt?id=ien.35556038198842&view=1up&seq=304. From p. 274: "Many of our supposed thousand million stars, perhaps a great majority of them, may be dark bodies; … "
- "A history of dark matter" (in en-us). https://arstechnica.com/science/2017/02/a-history-of-dark-matter/.
- Poincaré, H. (1906). "La Voie lactée et la théorie des gaz" (in fr). Bulletin de la Société astronomique de France 20: 153–165. https://babel.hathitrust.org/cgi/pt?id=uiug.30112110949630&view=1up&seq=171.
- Kapteyn, Jacobus Cornelius (1922). "First attempt at a theory of the arrangement and motion of the sidereal system". Astrophysical Journal 55: 302–327. doi:10.1086/142670. Bibcode: 1922ApJ....55..302K. "It is incidentally suggested when the theory is perfected it may be possible to determine the amount of dark matter from its gravitational effect.". (emphasis in original)
- Rosenberg, Leslie J (30 June 2014). "Status of the Axion Dark-Matter Experiment (ADMX)". 10th PATRAS Workshop on Axions, WIMPs and WISPs. p. 2. http://indico.cern.ch/event/300768/session/0/contribution/30/attachments/566901/780884/Rosenberg-Patras_30jun14.pdf.
- Lundmark, K. (1930-01-01). "Über die Bestimmung der Entfernungen, Dimensionen, Massen und Dichtigkeit fur die nächstgelegenen anagalacktischen Sternsysteme.". Meddelanden Fran Lunds Astronomiska Observatorium Serie I 125: 1–13. Bibcode: 1930MeLuF.125....1L. https://ui.adsabs.harvard.edu/abs/1930MeLuF.125....1L.
- Oort, J.H. (1932). "The force exerted by the stellar system in the direction perpendicular to the galactic plane and some related problems". Bulletin of the Astronomical Institutes of the Netherlands 6: 249–287. Bibcode: 1932BAN.....6..249O.
- "The hidden lives of galaxies: Hidden mass". NASA/GSFC. http://imagine.gsfc.nasa.gov/teachers/galaxies/imagine/hidden_mass.html.
- Kuijken, K.; Gilmore, G. (July 1989). "The Mass Distribution in the Galactic Disc – Part III – the Local Volume Mass Density". Monthly Notices of the Royal Astronomical Society 239 (2): 651–664. doi:10.1093/mnras/239.2.651. Bibcode: 1989MNRAS.239..651K.
- Zwicky, F. (1933). "Die Rotverschiebung von extragalaktischen Nebeln". Helvetica Physica Acta 6: 110–127. Bibcode: 1933AcHPh...6..110Z. From p 125: "Um, wie beobachtet, einen mittleren Dopplereffekt von 1000 km/sek oder mehr zu erhalten, müsste also die mittlere Dichte im Comasystem mindestens 400 mal grösser sein als die auf Grund von Beobachtungen an leuchtender Materie abgeleitete. Falls sich dies bewahrheiten sollte, würde sich also das überraschende Resultat ergeben, dass dunkel Materie in sehr viel grösserer Dichte vorhanden ist als leuchtende Materie." (In order to obtain an average Doppler effect of 1000 km/s or more, as observed, the average density in the Coma system would thus have to be at least 400 times greater than that derived on the basis of observations of luminous matter. If this were to be confirmed, the surprising result would then follow that dark matter is present in very much greater density than luminous matter.)
- Zwicky, F. (1937). "On the Masses of Nebulae and of Clusters of Nebulae". The Astrophysical Journal 86: 217–246. doi:10.1086/143864. Bibcode: 1937ApJ....86..217Z.
- Some details of Zwicky's calculation and of more modern values are given in Richmond, M., Using the virial theorem: the mass of a cluster of galaxies, http://spiff.rit.edu/classes/phys440/lectures/gal_clus/gal_clus.html, retrieved 10 July 2007
- Freese, Katherine (2014). The cosmic cocktail: Three parts dark matter. Princeton University Press. ISBN 978-1-4008-5007-5. https://books.google.com/books?id=c2B8AgAAQBAJ.
- Babcock, Horace W. (1939). "The rotation of the Andromeda Nebula". Lick Observatory Bulletin 19: 41–51. doi:10.5479/ADS/bib/1939LicOB.19.41B. Bibcode: 1939LicOB..19...41B.
- Oort, J.H. (April 1940). "Some problems concerning the structure and dynamics of the galactic system and the elliptical nebulae NGC 3115 and 4494". The Astrophysical Journal 91 (3): 273–306. doi:10.1086/144167. Bibcode: 1940ApJ....91..273O. https://openaccess.leidenuniv.nl/bitstream/handle/1887/8533/008_653_032.pdf?sequence=1.
- Freeman, K.C. (June 1970). "On the Disks of Spiral and S0 Galaxies". The Astrophysical Journal 160: 811–830. doi:10.1086/150474. Bibcode: 1970ApJ...160..811F.
- Overbye, Dennis (27 December 2016). "Vera Rubin, 88, Dies; Opened Doors in Astronomy, and for Women". The New York Times. https://www.nytimes.com/2016/12/27/science/vera-rubin-astronomist-who-made-the-case-for-dark-matter-dies-at-88.html.
- "First observational evidence of dark matter". http://www.darkmatterphysics.com/Galactic-rotation-curves-of-spiral-galaxies.htm.
- Rubin, Vera C.; Ford, W. Kent, Jr. (February 1970). "Rotation of the Andromeda Nebula from a Spectroscopic Survey of Emission Regions". The Astrophysical Journal 159: 379–403. doi:10.1086/150317. Bibcode: 1970ApJ...159..379R.
- Bosma, A. (1978). The distribution and kinematics of neutral hydrogen in spiral galaxies of various morphological types (PhD Thesis). Rijksuniversiteit Groningen.
- Rubin, V.; Thonnard, W.K. Jr.; Ford, N. (1980). "Rotational Properties of 21 Sc Galaxies with a Large Range of Luminosities and Radii from NGC 4605 (R = 4kpc) to UGC 2885 (R = 122kpc)". The Astrophysical Journal 238: 471. doi:10.1086/158003. Bibcode: 1980ApJ...238..471R.
- Randall 2015, pp. 13–14.
- Roberts, Morton S.; Davies, R.D.; Reddish, V.C. (1966). "A neutral hydrogen survey of the southern regions of the Andromeda nebula". Monthly Notices of the Royal Astronomical Society 133 (4): 359–387. doi:10.1093/mnras/133.4.359. Bibcode: 1966MNRAS.133..359G.
- Roberts, Morton S.; Whitehurst, Robert N. (October 1975). "The rotation curve and geometry of M 31 at large galactocentric distances". The Astrophysical Journal 201: 327–346. doi:10.1086/153889. Bibcode: 1975ApJ...201..327R.
- Rogstad, D.H.; Shostak, G. Seth (September 1972). "Gross properties of five Scd galaxies as determined from 21 centimeter observations". The Astrophysical Journal 176: 315–321. doi:10.1086/151636. Bibcode: 1972ApJ...176..315R.
- Randall 2015, pp. 14–16.
- Bergstrom, L. (2000). "Non-baryonic dark matter: Observational evidence and detection methods". Reports on Progress in Physics 63 (5): 793–841. doi:10.1088/0034-4885/63/5/2r3. Bibcode: 2000RPPh...63..793B.
- Baumann, Daniel. "Cosmology: Part III". Cambridge University. pp. 21–22. http://www.damtp.cam.ac.uk/user/db275/Cosmology/Lectures.pdf.
- "Serious Blow to Dark Matter Theories?" (Press release). European Southern Observatory. 18 April 2012.
- Corbelli, E.; Salucci, P. (2000). "The extended rotation curve and the dark matter halo of M33". Monthly Notices of the Royal Astronomical Society 311 (2): 441–447. doi:10.1046/j.1365-8711.2000.03075.x. Bibcode: 2000MNRAS.311..441C.
- Faber, S.M.; Jackson, R.E. (1976). "Velocity dispersions and mass-to-light ratios for elliptical galaxies". The Astrophysical Journal 204: 668–683. doi:10.1086/154215. Bibcode: 1976ApJ...204..668F.
- Binny, James; Merrifield, Michael (1998). Galactic Astronomy. Princeton University Press. pp. 712–713.
- Allen, Steven W.; Evrard, August E.; Mantz, Adam B. (2011). "Cosmological Parameters from Clusters of Galaxies". Annual Review of Astronomy and Astrophysics 49 (1): 409–470. doi:10.1146/annurev-astro-081710-102514. Bibcode: 2011ARA&A..49..409A.
- "Dark matter may be smoother than expected – Careful study of large area of sky imaged by VST reveals intriguing result". https://www.eso.org/public/news/eso1642/.
- Taylor, A.N. (1998). "Gravitational lens magnification and the mass of Abell 1689". The Astrophysical Journal 501 (2): 539–553. doi:10.1086/305827. Bibcode: 1998ApJ...501..539T.
- Wu, X.; Chiueh, T.; Fang, L.; Xue, Y. (1998). "A comparison of different cluster mass estimates: consistency or discrepancy?". Monthly Notices of the Royal Astronomical Society 301 (3): 861–871. doi:10.1046/j.1365-8711.1998.02055.x. Bibcode: 1998MNRAS.301..861W.
- Cho, Adrian (2017). "Scientists unveil the most detailed map of dark matter to date". Science. doi:10.1126/science.aal0847. http://www.sciencemag.org/news/2017/03/scientists-unveil-most-detailed-map-dark-matter-date.
- Natarajan, Priyamvada; Chadayammuri, Urmila; Jauzac, Mathilde; Richard, Johan; Kneib, Jean-Paul; Ebeling, Harald et al. (2017). "Mapping substructure in the HST Frontier Fields cluster lenses and in cosmological simulations". Monthly Notices of the Royal Astronomical Society 468 (2): 1962. doi:10.1093/mnras/stw3385. Bibcode: 2017MNRAS.468.1962N. http://dro.dur.ac.uk/22700/1/22700.pdf.
- Refregier, A. (2003). "Weak gravitational lensing by large-scale structure". Annual Review of Astronomy and Astrophysics 41 (1): 645–668. doi:10.1146/annurev.astro.41.111302.102207. Bibcode: 2003ARA&A..41..645R.
- "Quasars, lensing, and dark matter". Annenberg Foundation. 2017. https://www.learner.org/courses/physics/unit/text.html?unit=10&secNum=4.
- Myslewski, Rik (14 October 2011). "Hubble snaps dark matter warping spacetime". The Register (UK). https://www.theregister.co.uk/2011/10/14/hubble_images_gravitational_lensing/.
- "New dark matter map reveals cosmic mystery". 28 May 2021. https://www.bbc.com/news/science-environment-57244708.
- Sungwook E. Hong (2021). "Revealing the Local Cosmic Web from Galaxies by Deep Learning". 913. The Astrophysical Journal. doi:10.3847/1538-4357/abf040.
- The details are technical. For an intermediate-level introduction, see Hu, Wayne (2001). "Intermediate Guide to the Acoustic Peaks and Polarization". http://background.uchicago.edu/~whu/intermediate/intermediate.html.
- Hinshaw, G. (2009). "Five-year Wilkinson microwave anisotropy probe (WMAP) observations: Data processing, sky maps, and basic results". The Astrophysical Journal Supplement 180 (2): 225–245. doi:10.1088/0067-0049/180/2/225. Bibcode: 2009ApJS..180..225H.
- Ade, P.A.R. (2016). "Planck 2015 results. XIII. Cosmological parameters". Astron. Astrophys. 594 (13): A13. doi:10.1051/0004-6361/201525830. Bibcode: 2016A&A...594A..13P.
- Skordis, C. (2006). "Large scale structure in Bekenstein's theory of relativistic modified Newtonian dynamics". Phys. Rev. Lett. 96 (1): 011301. doi:10.1103/PhysRevLett.96.011301. PMID 16486433. Bibcode: 2006PhRvL..96a1301S.
- "Hubble Maps the Cosmic Web of "Clumpy" Dark Matter in 3-D" (Press release). NASA. 7 January 2007. Archived from the original on May 21, 2013.
- Jaffe, A.H.. "Cosmology 2012: Lecture Notes". http://astro.imperial.ac.uk/sites/default/files/cosmology.pdf.
- Low, L.F. (12 October 2016). "Constraints on the composite photon theory". Modern Physics Letters A 31 (36): 1675002. doi:10.1142/S021773231675002X. Bibcode: 2016MPLA...3175002L. https://zenodo.org/record/896052.
- Clowe, Douglas (2006). "A Direct Empirical Proof of the Existence of Dark Matter". The Astrophysical Journal Letters 648 (2): L109–L113. doi:10.1086/508162. Bibcode: 2006ApJ...648L.109C.
- Lee, Chris (21 September 2017). "Science-in-progress: Did the Bullet Cluster withstand scrutiny?". https://arstechnica.com/science/2017/09/science-in-progress-did-the-bullet-cluster-withstand-scrutiny/.
- Siegel, Ethan (9 November 2017). "The Bullet Cluster proves dark matter exists, but not for the reason most physicists think". Forbes. https://www.forbes.com/sites/startswithabang/2017/11/09/the-bullet-cluster-proves-dark-matter-exists-but-not-for-the-reason-most-physicists-think/#3032b6081738.
- Markevitch, M.; Randall, S.; Clowe, D.; Gonzalez, A.; Bradac, M. (16–23 July 2006). "Dark matter and the Bullet Cluster". 36th COSPAR Scientific Assembly. Beijing, China. http://cosis.net/abstracts/COSPAR2006/02655/COSPAR2006-A-02655.pdf. Abstract only
- Planck Collaboration; Aghanim, N.; Akrami, Y.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Ballardini, M.; Banday, A. J. et al. (2020). "Planck 2018 results. VI. Cosmological parameters". Astronomy & Astrophysics 641: A6. doi:10.1051/0004-6361/201833910. Bibcode: 2020A&A...641A...6P.
- Kowalski, M. (2008). "Improved Cosmological Constraints from New, Old, and Combined Supernova Data Sets". The Astrophysical Journal 686 (2): 749–778. doi:10.1086/589937. Bibcode: 2008ApJ...686..749K.
- "Will the Universe expand forever?". NASA. 24 January 2014. https://map.gsfc.nasa.gov/universe/uni_shape.html.
- "Our flat universe". FermiLab/SLAC. 7 April 2015. https://www.symmetrymagazine.org/article/april-2015/our-flat-universe.
- Yoo, Marcus Y. (2011). "Unexpected connections". Engineering & Science 74 (1): 30.
- "Planck Publications: Planck 2015 Results". European Space Agency. February 2015. http://www.cosmos.esa.int/web/planck/publications.
- Percival, W.J. (2007). "Measuring the Baryon Acoustic Oscillation scale using the Sloan Digital Sky Survey and 2dF Galaxy Redshift Survey". Monthly Notices of the Royal Astronomical Society 381 (3): 1053–1066. doi:10.1111/j.1365-2966.2007.12268.x. Bibcode: 2007MNRAS.381.1053P.
- Komatsu, E. (2009). "Five-Year Wilkinson Microwave Anisotropy Probe Observations: Cosmological Interpretation". The Astrophysical Journal Supplement 180 (2): 330–376. doi:10.1088/0067-0049/180/2/330. Bibcode: 2009ApJS..180..330K.
- Peacock, J. (2001). "A measurement of the cosmological mass density from clustering in the 2dF Galaxy Redshift Survey". Nature 410 (6825): 169–173. doi:10.1038/35065528. PMID 11242069. Bibcode: 2001Natur.410..169P.
- Viel, M.; Bolton, J.S.; Haehnelt, M.G. (2009). "Cosmological and astrophysical constraints from the Lyman α forest flux probability distribution function". Monthly Notices of the Royal Astronomical Society 399 (1): L39–L43. doi:10.1111/j.1745-3933.2009.00720.x. Bibcode: 2009MNRAS.399L..39V.
- University of Amsterdam. "A new era in the quest for dark matter". Phys.org. https://phys.org/news/2018-10-era-quest-dark.html.
- Espinosa, J. R.; Racco, D.; Riotto, A. (23 March 2018). "A Cosmological Signature of the Standard Model Higgs Vacuum Instability: Primordial Black Holes as Dark Matter". Physical Review Letters 120 (12): 121301. doi:10.1103/PhysRevLett.120.121301. PMID 29694085. Bibcode: 2018PhRvL.120l1301E.
- Clesse, Sebastien; García-Bellido, Juan (2018). "Seven Hints for Primordial Black Hole Dark Matter". Physics of the Dark Universe 22: 137–146. doi:10.1016/j.dark.2018.08.004. Bibcode: 2018PDU....22..137C.
- Lacki, Brian C.; Beacom, John F. (12 August 2010). "Primordial Black Holes as Dark Matter: Almost All or Almost Nothing" (in en). The Astrophysical Journal 720 (1): L67–L71. doi:10.1088/2041-8205/720/1/L67. ISSN 2041-8205. Bibcode: 2010ApJ...720L..67L.
- Kashlinsky, A. (23 May 2016). "LIGO gravitational wave detection, primordial black holes and the near-IR cosmic infrared background anisotropies". The Astrophysical Journal 823 (2): L25. doi:10.3847/2041-8205/823/2/L25. ISSN 2041-8213. Bibcode: 2016ApJ...823L..25K.
- Frampton, Paul H.; Kawasaki, Masahiro; Takahashi, Fuminobu; Yanagida, Tsutomu T. (22 April 2010). "Primordial Black Holes as All Dark Matter". Journal of Cosmology and Astroparticle Physics 2010 (4): 023. doi:10.1088/1475-7516/2010/04/023. ISSN 1475-7516. Bibcode: 2010JCAP...04..023F.
- Carneiro, S.; de Holanda, P.C.; Saa, A. (2021). "Neutrino primordial Planckian black holes". Physics Letters B822: 136670. doi:10.1016/j.physletb.2021.136670. ISSN 0370-2693. Bibcode: 2021PhLB..82236670C.
- "Baryonic Matter". Swinburne University of Technology. http://astronomy.swin.edu.au/cosmos/B/Baryonic+Matter.
- Randall 2015, p. 286.
- Weiss, Achim (2006). Big bang nucleosynthesis: Cooking up the first light elements. 2. p. 1017. http://www.einstein-online.info/spotlights/BBN.
- Raine, D.; Thomas, T. (2001). An Introduction to the Science of Cosmology. IOP Publishing. p. 30. ISBN 978-0-7503-0405-4. OCLC 864166846.
- Tisserand, P.; Le Guillou, L.; Afonso, C.; Albert, J.N.; Andersen, J.; Ansari, R. et al. (2007). "Limits on the Macho content of the Galactic Halo from the EROS-2 Survey of the Magellanic Clouds". Astronomy and Astrophysics 469 (2): 387–404. doi:10.1051/0004-6361:20066017. Bibcode: 2007A&A...469..387T. https://www.researchgate.net/publication/41714676.
- Graff, D.S.; Freese, K. (1996). "Analysis of a Hubble Space Telescope Search for Red Dwarfs: Limits on Baryonic Matter in the Galactic Halo". The Astrophysical Journal 456 (1996): L49. doi:10.1086/309850. Bibcode: 1996ApJ...456L..49G.
- Najita, J.R.; Tiede, G.P.; Carr, J.S. (2000). "From Stars to Superplanets: The Low‐Mass Initial Mass Function in the Young Cluster IC 348". The Astrophysical Journal 541 (2): 977–1003. doi:10.1086/309477. Bibcode: 2000ApJ...541..977N.
- Wyrzykowski, L.; Skowron, J.; Kozlowski, S.; Udalski, A.; Szymanski, M.K.; Kubiak, M. et al. (2011). "The OGLE View of Microlensing towards the Magellanic Clouds. IV. OGLE-III SMC Data and Final Conclusions on MACHOs". Monthly Notices of the Royal Astronomical Society 416 (4): 2949–2961. doi:10.1111/j.1365-2966.2011.19243.x. Bibcode: 2011MNRAS.416.2949W.
- Freese, Katherine; Fields, Brian; Graff, David (2000). "Death of stellar baryonic dark matter candidates". arXiv:astro-ph/0007444.
- Freese, Katherine; Fields, Brian; Graff, David (1999). "Death of Stellar Baryonic Dark Matter". The First Stars. ESO Astrophysics Symposia. 4–6. doi:10.1007/10719504_3. ISBN 978-3-540-67222-7. Bibcode: 2000fist.conf...18F.
- Canetti, L.; Drewes, M.; Shaposhnikov, M. (2012). "Matter and Antimatter in the Universe". New J. Phys. 14 (9): 095012. doi:10.1088/1367-2630/14/9/095012. Bibcode: 2012NJPh...14i5012C.
- Guiot, B; Borquez, A.; Deur, A.; Werner, K. (2020). "Graviballs and Dark Matter". JHEP 2020 (11): 159. doi:10.1007/JHEP11(2020)159. Bibcode: 2020JHEP...11..159G. .
- Overduin, J. M.; Wesson, P. S. (November 2004). "Dark Matter and Background Light". Physics Reports 402 (5–6): 267–406. doi:10.1016/j.physrep.2004.07.006. Bibcode: 2004PhR...402..267O.
- Bertone, G.; Merritt, D. (2005). "Dark Matter Dynamics and Indirect Detection". Modern Physics Letters A 20 (14): 1021–1036. doi:10.1142/S0217732305017391. Bibcode: 2005MPLA...20.1021B.
- "Are there any dark stars or dark galaxies made of dark matter?". http://curious.astro.cornell.edu/about-us/95-the-universe/galaxies/general-questions/508-are-there-any-dark-stars-or-dark-galaxies-made-of-dark-matter-advanced.
- Buckley, Matthew R.; Difranzo, Anthony (1 February 2018). "Synopsis: A Way to Cool Dark Matter". Physical Review Letters 120 (5): 051102. doi:10.1103/PhysRevLett.120.051102. PMID 29481169. Bibcode: 2018PhRvL.120e1102B. https://physics.aps.org/articles/v11/s15. "One widely held belief about dark matter is it cannot cool off by radiating energy. If it could, then it might bunch together and create compact objects in the same way baryonic matter forms planets, stars, and galaxies. Observations so far suggest dark matter doesn't do that – it resides only in diffuse halos ... As a result, it is extremely unlikely there are very dense objects like stars made out of entirely (or even mostly) dark matter.".
- Siegel, Ethan (28 October 2016). "Why doesn't dark matter form black holes?". Forbes. https://www.forbes.com/sites/startswithabang/2016/10/28/why-doesnt-dark-matter-form-black-holes/#4e5014943de1.
- Cho, Adrian (9 February 2017). "Is dark matter made of black holes?". Science. doi:10.1126/science.aal0721.
- "Black holes can't explain dark matter". astronomy.com. 18 October 2018. http://astronomy.com/news/2018/10/can-black-holes-explain-dark-matter.
- "Aging Voyager 1 spacecraft undermines idea that dark matter is tiny black holes". sciencemag.org. 9 January 2019. https://www.sciencemag.org/news/2019/01/aging-voyager-1-spacecraft-undermines-idea-dark-matter-tiny-black-holes.
- Hall, Shannon. "There could be entire stars and planets made out of dark matter". https://www.newscientist.com/article/2160305-there-could-be-entire-stars-and-planets-made-out-of-dark-matter/.
- Buckley, Matthew R.; Difranzo, Anthony (2018). "Collapsed Dark Matter Structures". Physical Review Letters 120 (5): 051102. doi:10.1103/PhysRevLett.120.051102. PMID 29481169. Bibcode: 2018PhRvL.120e1102B.
- Niikura, Hiroko (1 April 2019). "Microlensing constraints on primordial black holes with Subaru/HSC Andromeda observations". Nature Astronomy 3 (6): 524–534. doi:10.1038/s41550-019-0723-1. Bibcode: 2019NatAs...3..524N.
- Katz, Andrey; Kopp, Joachim; Sibiryakov, Sergey; Xue, Wei (2018-12-05). "Femtolensing by dark matter revisited". Journal of Cosmology and Astroparticle Physics 2018 (12): 005. doi:10.1088/1475-7516/2018/12/005. ISSN 1475-7516. Bibcode: 2018JCAP...12..005K. http://stacks.iop.org/1475-7516/2018/i=12/a=005?key=crossref.dcb1e788286d8d75d0c7e7f35fe588eb.
- Montero-Camacho, Paulo; Fang, Xiao; Vasquez, Gabriel; Silva, Makana; Hirata, Christopher M. (2019-08-23). "Revisiting constraints on asteroid-mass primordial black holes as dark matter candidates". Journal of Cosmology and Astroparticle Physics 2019 (8): 031. doi:10.1088/1475-7516/2019/08/031. ISSN 1475-7516. Bibcode: 2019JCAP...08..031M.
- Silk, Joseph (2000). "IX". The Big Bang: Third Edition. Henry Holt and Company. ISBN 978-0-8050-7256-3. https://books.google.com/books?id=XLwe1lUmz5kC&pg=PA82.
- Vittorio, N.; J. Silk (1984). "Fine-scale anisotropy of the cosmic microwave background in a universe dominated by cold dark matter". Astrophysical Journal Letters 285: L39–L43. doi:10.1086/184361. Bibcode: 1984ApJ...285L..39V.
- Umemura, Masayuki; Satoru Ikeuchi (1985). "Formation of Subgalactic Objects within Two-Component Dark Matter". Astrophysical Journal 299: 583–592. doi:10.1086/163726. Bibcode: 1985ApJ...299..583U.
- Davis, M.; Efstathiou, G.; Frenk, C.S.; White, S.D.M. (15 May 1985). "The evolution of large-scale structure in a universe dominated by cold dark matter". Astrophysical Journal 292: 371–394. doi:10.1086/163168. Bibcode: 1985ApJ...292..371D.
- Hawkins, M.R.S. (2011). "The case for primordial black holes as dark matter". Monthly Notices of the Royal Astronomical Society 415 (3): 2744–2757. doi:10.1111/j.1365-2966.2011.18890.x. Bibcode: 2011MNRAS.415.2744H.
- Hansson, J.; Sandin, F. (2005). "Preon stars: a new class of cosmic compact objects". Physics Letters B 616 (1–2): 1–7. doi:10.1016/j.physletb.2005.04.034. Bibcode: 2005PhLB..616....1H.
- Carr, B.J. (2010). "New cosmological constraints on primordial black holes". Physical Review D 81 (10): 104019. doi:10.1103/PhysRevD.81.104019. Bibcode: 2010PhRvD..81j4019C.
- Peter, A.H.G. (2012). "Dark matter: A brief review". arXiv:1201.3942 [astro-ph.CO].
- Garrett, Katherine; Dūda, Gintaras (2011). "Dark Matter: A Primer". Advances in Astronomy 2011 (968283): 1–22. doi:10.1155/2011/968283. Bibcode: 2011AdAst2011E...8G. "MACHOs can only account for a very small percentage of the nonluminous mass in our galaxy, revealing that most dark matter cannot be strongly concentrated or exist in the form of baryonic astrophysical objects. Although microlensing surveys rule out baryonic objects like brown dwarfs, black holes, and neutron stars in our galactic halo, can other forms of baryonic matter make up the bulk of dark matter? The answer, surprisingly, is 'no' ...".
- Bertone, G. (2010). "The moment of truth for WIMP dark matter". Nature 468 (7322): 389–393. doi:10.1038/nature09509. PMID 21085174. Bibcode: 2010Natur.468..389B.
- Olive, Keith A (2003). "TASI Lectures on Dark Matter". p. 21. arXiv:astro-ph/0301505.
- Jungman, Gerard; Kamionkowski, Marc; Griest, Kim (1 March 1996). "Supersymmetric dark matter". Physics Reports 267 (5–6): 195–373. doi:10.1016/0370-1573(95)00058-5. Bibcode: 1996PhR...267..195J.
- "Neutrinos as dark matter". Astro.ucla.edu. 21 September 1998. http://www.astro.ucla.edu/~wright/neutrinos.html.
- Gaitskell, Richard J. (2004). "Direct Detection of Dark Matter". Annual Review of Nuclear and Particle Science 54: 315–359. doi:10.1146/annurev.nucl.54.070103.181244. Bibcode: 2004ARNPS..54..315G.
- "Neutralino Dark Matter". http://www.picassoexperiment.ca/dm_neutralino.php. Griest, Kim. "WIMPs and MACHOs". http://www.astro.caltech.edu/~george/ay20/eaa-wimps-machos.pdf.
- Drees, M.; Gerbier, G. (2015). "Dark Matter". Chin. Phys. C 38: 090001. http://pdg.lbl.gov/2015/reviews/rpp2015-rev-dark-matter.pdf.
- Bernabei, R.; Belli, P.; Cappella, F.; Cerulli, R.; Dai, C.J.; d’Angelo, A. et al. (2008). "First results from DAMA/LIBRA and the combined results with DAMA/NaI". Eur. Phys. J. C 56 (3): 333–355. doi:10.1140/epjc/s10052-008-0662-y. Bibcode: 2008EPJC...56..333B.
- Drukier, A.; Freese, K.; Spergel, D. (1986). "Detecting Cold Dark Matter Candidates". Physical Review D 33 (12): 3495–3508. doi:10.1103/PhysRevD.33.3495. PMID 9956575. Bibcode: 1986PhRvD..33.3495D.
- Davis, Jonathan H. (2015). "The past and future of light dark matter direct detection". Int. J. Mod. Phys. A 30 (15): 1530038. doi:10.1142/S0217751X15300380. Bibcode: 2015IJMPA..3030038D.
- Aprile, E. (2017). "Search for electronic recoil event rate modulation with 4 years of XENON100 data". Phys. Rev. Lett. 118 (10): 101101. doi:10.1103/PhysRevLett.118.101101. PMID 28339273. Bibcode: 2017PhRvL.118j1101A.
- Stonebraker, Alan (3 January 2014). "Synopsis: Dark-Matter Wind Sways through the Seasons". Physics – Synopses (American Physical Society). doi:10.1103/PhysRevLett.112.011301.
- Lee, Samuel K.; Lisanti, Mariangela; Peter, Annika H.G.; Safdi, Benjamin R. (3 January 2014). "Effect of Gravitational Focusing on Annual Modulation in Dark-Matter Direct-Detection Experiments". Phys. Rev. Lett. 112 (1): 011301 [5 pages]. doi:10.1103/PhysRevLett.112.011301. PMID 24483881. Bibcode: 2014PhRvL.112a1301L.
- The Dark Matter Group. "An Introduction to Dark Matter". Dark Matter Research (Sheffield: University of Sheffield). http://www.hep.shef.ac.uk/research/dm/intro.php.
- "Blowing in the Wind". Kavli News (Sheffield: Kavli Foundation). http://www.kavlifoundation.org/science-spotlights/blowing-wind. "Scientists at Kavli MIT are working on ... a tool to track the movement of dark matter."
- "Dark matter even darker than once thought". http://www.spacetelescope.org/news/heic1506/.
- Bertone, Gianfranco (2010). "Dark Matter at the Centers of Galaxies". Particle Dark Matter: Observations, Models and Searches. Cambridge University Press. pp. 83–104. ISBN 978-0-521-76368-4. Bibcode: 2010arXiv1001.3706M. https://books.google.com/books?id=JkUgAwAAQBAJ&pg=PA83.
- Ellis, J.; Flores, R.A.; Freese, K.; Ritz, S.; Seckel, D.; Silk, J. (1988). "Cosmic ray constraints on the annihilations of relic particles in the galactic halo". Physics Letters B 214 (3): 403–412. doi:10.1016/0370-2693(88)91385-8. Bibcode: 1988PhLB..214..403E. http://cds.cern.ch/record/190709/files/198809398.pdf.
- Freese, K. (1986). "Can Scalar Neutrinos or Massive Dirac Neutrinos be the Missing Mass?". Physics Letters B 167 (3): 295–300. doi:10.1016/0370-2693(86)90349-7. Bibcode: 1986PhLB..167..295F.
- Randall 2015, p. 298.
- Sokol, Joshua (20 February 2016). "Surfing gravity's waves". New Scientist (3061). https://www.newscientist.com/article/2077800-what-will-gravitational-waves-tell-us-about-the-universe.
- "Did gravitational wave detector find dark matter?". Johns Hopkins University. 15 June 2016. http://releases.jhu.edu/2016/06/15/did-gravitational-wave-detector-find-dark-matter/. "While their existence has not been established with certainty, primordial black holes have in the past been suggested as a possible solution to the dark matter mystery. Because there is so little evidence of them, though, the primordial black hole–dark matter hypothesis has not gained a large following among scientists. The LIGO findings, however, raise the prospect anew, especially as the objects detected in that experiment conform to the mass predicted for dark matter. Predictions made by scientists in the past held conditions at the birth of the universe would produce many of these primordial black holes distributed approximately evenly in the universe, clustering in halos around galaxies. All this would make them good candidates for dark matter."
- Bird, Simeon; Cholis, Illian (2016). "Did LIGO detect dark matter?". Physical Review Letters 116 (20): 201301. doi:10.1103/PhysRevLett.116.201301. PMID 27258861. Bibcode: 2016PhRvL.116t1301B.
- Stecker, F.W.; Hunter, S.; Kniffen, D. (2008). "The likely cause of the EGRET GeV anomaly and its implications". Astroparticle Physics 29 (1): 25–29. doi:10.1016/j.astropartphys.2007.11.002. Bibcode: 2008APh....29...25S.
- Atwood, W.B.; Abdo, A.A.; Ackermann, M.; Althouse, W.; Anderson, B.; Axelsson, M. et al. (2009). "The large area telescope on the Fermi Gamma-ray Space Telescope Mission". Astrophysical Journal 697 (2): 1071–1102. doi:10.1088/0004-637X/697/2/1071. Bibcode: 2009ApJ...697.1071A.
- Weniger, Christoph (2012). "A tentative gamma-ray line from dark matter annihilation at the Fermi Large Area Telescope". Journal of Cosmology and Astroparticle Physics 2012 (8): 7. doi:10.1088/1475-7516/2012/08/007. Bibcode: 2012JCAP...08..007W.
- Cartlidge, Edwin (24 April 2012). "Gamma rays hint at dark matter". Institute of Physics. http://physicsworld.com/cws/article/news/2012/apr/24/gamma-rays-hint-at-dark-matter.
- Albert, J.; Aliu, E.; Anderhub, H.; Antoranz, P.; Backes, M.; Baixeras, C. et al. (2008). "Upper Limit for γ‐Ray Emission above 140 GeV from the Dwarf Spheroidal Galaxy Draco". The Astrophysical Journal 679 (1): 428–431. doi:10.1086/529135. Bibcode: 2008ApJ...679..428A.
- Aleksić, J.; Antonelli, L.A.; Antoranz, P.; Backes, M.; Baixeras, C.; Balestra, S. et al. (2010). "Magic Gamma-Ray Telescope observation of the Perseus Cluster of galaxies: Implications for cosmic rays, dark matter, and NGC 1275". The Astrophysical Journal 710 (1): 634–647. doi:10.1088/0004-637X/710/1/634. Bibcode: 2010ApJ...710..634A.
- Adriani, O.; Barbarino, G.C.; Bazilevskaya, G.A.; Bellotti, R.; Boezio, M.; Bogomolov, E.A. et al. (2009). "An anomalous positron abundance in cosmic rays with energies 1.5–100 GeV". Nature 458 (7238): 607–609. doi:10.1038/nature07942. PMID 19340076. Bibcode: 2009Natur.458..607A.
- Aguilar, M. (3 April 2013). "First Result from the Alpha Magnetic Spectrometer on the International Space Station: Precision Measurement of the Positron Fraction in Primary Cosmic Rays of 0.5–350 GeV". Physical Review Letters 110 (14): 141102. doi:10.1103/PhysRevLett.110.141102. PMID 25166975. Bibcode: 2013PhRvL.110n1102A.
- AMS Collaboration (3 April 2013). "First Result from the Alpha Magnetic Spectrometer Experiment". http://www.ams02.org/2013/04/first-results-from-the-alpha-magnetic-spectrometer-ams-experiment/.
- Heilprin, John; Borenstein, Seth (3 April 2013). "Scientists find hint of dark matter from cosmos". Associated Press. http://apnews.excite.com/article/20130403/DA5E6JAG3.html.
- Amos, Jonathan (3 April 2013). "Alpha Magnetic Spectrometer zeroes in on dark matter". BBC. https://www.bbc.co.uk/news/science-environment-22016504.
- Perrotto, Trent J.; Byerly, Josh (2 April 2013). "NASA TV Briefing Discusses Alpha Magnetic Spectrometer Results". http://www.nasa.gov/home/hqnews/2013/apr/HQ_M13-054_AMS_Findings_Briefing.html.
- Overbye, Dennis (3 April 2013). "New Clues to the Mystery of Dark Matter". The New York Times. https://www.nytimes.com/2013/04/04/science/space/new-clues-to-the-mystery-of-dark-matter.html.
- Kane, G.; Watson, S. (2008). "Dark Matter and LHC:. what is the Connection?". Modern Physics Letters A 23 (26): 2103–2123. doi:10.1142/S0217732308028314. Bibcode: 2008MPLA...23.2103K.
- Fox, P.J.; Harnik, R.; Kopp, J.; Tsai, Y. (2011). "LEP Shines Light on Dark Matter". Phys. Rev. D 84 (1): 014028. doi:10.1103/PhysRevD.84.014028. Bibcode: 2011PhRvD..84a4028F.
- Peebles, P. J. E. (December 2004). "Probing General Relativity on the Scales of Cosmology". Testing general relativity on the scales of cosmology. 106–117. doi:10.1142/9789812701688_0010. ISBN 978-981-256-424-5. Bibcode: 2005grg..conf..106P.
- For a review, see: Kroupa, Pavel (December 2012). "The failures of the Standard Model of Cosmology require a new paradigm". International Journal of Modern Physics D 21 (4): 1230003. doi:10.1142/S0218271812300030. Bibcode: 2012IJMPD..2130003K.
- For a review, see: Salvatore Capozziello; Mariafelicia De Laurentis (October 2012). "The dark matter problem from f(R) gravity viewpoint". Annalen der Physik 524 (9–10): 545. doi:10.1002/andp.201200109. Bibcode: 2012AnP...524..545C.
- "Bringing balance to the Universe". University of Oxford. https://www.ox.ac.uk/news/2018-12-05-bringing-balance-universe.
- "Bringing balance to the universe: New theory could explain missing 95 percent of the cosmos". Phys.Org. https://phys.org/news/2018-12-universe-theory-percent-cosmos.html.
- Farnes, J.S. (2018). "A Unifying Theory of Dark Energy and Dark Matter: Negative Masses and Matter Creation within a Modified ΛCDM Framework". Astronomy & Astrophysics 620: A92. doi:10.1051/0004-6361/201832898. Bibcode: 2018A&A...620A..92F.
- "New theory of gravity might explain dark matter". November 2016. https://phys.org/news/2016-11-theory-gravity-dark.html.
- Mannheim, Phillip D. (April 2006). "Alternatives to dark matter and dark energy". Progress in Particle and Nuclear Physics 56 (2): 340–445. doi:10.1016/j.ppnp.2005.08.001. Bibcode: 2006PrPNP..56..340M.
- Joyce, Austin (March 2015). "Beyond the Cosmological Standard Model". Physics Reports 568: 1–98. doi:10.1016/j.physrep.2014.12.002. Bibcode: 2015PhR...568....1J.
- "Verlinde's new theory of gravity passes first test". 16 December 2016. http://phys.org/news/2016-12-verlinde-theory-gravity.html.
- Brouwer, Margot M. (April 2017). "First test of Verlinde's theory of Emergent Gravity using Weak Gravitational Lensing measurements". Monthly Notices of the Royal Astronomical Society 466 (3): 2547–2559. doi:10.1093/mnras/stw3192. Bibcode: 2017MNRAS.466.2547B.
- "First test of rival to Einstein's gravity kills off dark matter". 15 December 2016. https://www.newscientist.com/article/2116446-first-test-of-rival-to-einsteins-gravity-kills-off-dark-matter/.
- "Unique prediction of 'modified gravity' challenges dark matter". ScienceDaily. 16 December 2020. https://www.sciencedaily.com/releases/2020/12/201216155158.htm.
- Chae, Kyu-Hyun (20 November 2020). "Testing the Strong Equivalence Principle: Detection of the External Field Effect in Rotationally Supported Galaxies". Astrophysical Journal 904 (1): 51. doi:10.3847/1538-4357/abbb96. Bibcode: 2020ApJ...904...51C.
- Sean Carroll (9 May 2012). "Dark matter vs. modified gravity: A trialogue". http://www.preposterousuniverse.com/blog/2012/05/09/dark-matter-vs-modified-gravity-a-trialogue/.
- "First 3D map of the Universe's dark matter scaffolding" (in en). https://www.esa.int/Science_Exploration/Space_Science/First_3D_map_of_the_Universe_s_dark_matter_scaffolding.
- Massey, Richard; Rhodes, Jason; Ellis, Richard; Scoville, Nick; Leauthaud, Alexie; Finoguenov, Alexis; Capak, Peter; Bacon, David et al. (January 2007). "Dark matter maps reveal cosmic scaffolding" (in en). Nature 445 (7125): 286–290. doi:10.1038/nature05497. ISSN 1476-4687. PMID 17206154. Bibcode: 2007Natur.445..286M. https://www.nature.com/articles/nature05497.
- "News CFHT - Astronomers reach new frontiers of dark matter". https://www.cfht.hawaii.edu/en/news/CFHTLens/.
- Heymans, Catherine; Van Waerbeke, Ludovic; Miller, Lance; Erben, Thomas; Hildebrandt, Hendrik; Hoekstra, Henk; Kitching, Thomas D.; Mellier, Yannick et al. (2012-11-21). "CFHTLenS: the Canada–France–Hawaii Telescope Lensing Survey: CFHTLenS" (in en). Monthly Notices of the Royal Astronomical Society 427 (1): 146–166. doi:10.1111/j.1365-2966.2012.21952.x. https://academic.oup.com/mnras/article-lookup/doi/10.1111/j.1365-2966.2012.21952.x.
- "KiDS". https://kids.strw.leidenuniv.nl/pr_july2015.php.
- Kuijken, Konrad; Heymans, Catherine; Hildebrandt, Hendrik; Nakajima, Reiko; Erben, Thomas; Jong, Jelte T. A.; Viola, Massimo; Choi, Ami et al. (10 October 2015). "Gravitational lensing analysis of the Kilo-Degree Survey" (in en). Monthly Notices of the Royal Astronomical Society 454 (4): 3500–3532. doi:10.1093/mnras/stv2140. ISSN 0035-8711. https://academic.oup.com/mnras/article-lookup/doi/10.1093/mnras/stv2140.
- University, Carnegie Mellon (26 September 2018). "Hyper Suprime-Cam Survey Maps Dark Matter in the Universe - News - Carnegie Mellon University" (in en). http://www.cmu.edu/news/stories/archives/2018/october/dark-matter-survey.html.
- Hikage, Chiaki; Oguri, Masamune; Hamana, Takashi; More, Surhud; Mandelbaum, Rachel; Takada, Masahiro; Köhlinger, Fabian; Miyatake, Hironao et al. (2019-04-01). "Cosmology from cosmic shear power spectra with Subaru Hyper Suprime-Cam first-year data" (in en). Publications of the Astronomical Society of Japan 71 (2): 43. doi:10.1093/pasj/psz010. ISSN 0004-6264. https://academic.oup.com/pasj/article/doi/10.1093/pasj/psz010/5370019.
- Jeffrey, N; Gatti, M; Chang, C; Whiteway, L; Demirbozan, U; Kovacs, A; Pollina, G; Bacon, D et al. (2021-06-25). "Dark Energy Survey Year 3 results: Curved-sky weak lensing mass map reconstruction" (in en). Monthly Notices of the Royal Astronomical Society 505 (3): 4626–4645. doi:10.1093/mnras/stab1495. ISSN 0035-8711. https://academic.oup.com/mnras/article/505/3/4626/6287258.
- Castelvecchi, Davide (2021-05-28). "The most detailed 3D map of the Universe ever made" (in en). Nature: d41586–021–01466-1. doi:10.1038/d41586-021-01466-1. ISSN 0028-0836. PMID 34050347. http://www.nature.com/articles/d41586-021-01466-1.
- Hossenfelder, Sabine; McGaugh, Stacy S. (August 2018). "Is dark matter real?". Scientific American 319 (2): 36–43.
- Dark matter at Curlie
- "A history of dark matter". February 2017. https://arstechnica.com/science/2017/02/a-history-of-dark-matter/.
- "What is dark matter?". http://archive.cosmosmagazine.com/features/what-dark-matter/.
- “Missing Dark Matter” in a far-away galaxy, Tech Explorer news item, from a 2020 Astrophysical Journalarticle, DOI: 10.3847/1538-4357/abc340
- Kroupa, Pavel (18 August 2010). "The Dark Matter Crisis". http://www.scilogs.com/the-dark-matter-crisis/2010/08/18/is-lambdacdm-or-standard-cosmology-a-4th-order-speculation-and-ought-it-be-further-researched/.
- "Helmholtz Alliance for Astroparticle Physics". 26 January 2018. http://www.hap-astroparticle.org/.
- "NASA finds direct proof of dark matter" (Press release). NASA. 21 August 2006.
- Tuttle, Kelen (22 August 2006). "Dark Matter Observed". SLAC (Stanford Linear Accelerator Center) Today. http://today.slac.stanford.edu/feature/darkmatter.asp.
- "Astronomers claim first 'dark galaxy' find". New Scientist. 23 February 2005. https://www.newscientist.com/article/dn7056-astronomers-claim-first-dark-galaxy-find/.
- Sample, Ian (17 December 2009). "Dark Matter Detected". Guardian (London, UK). https://www.theguardian.com/science/2009/dec/17/dark-matter-detected.
- Tremaine, Scott. lecture on dark matter (Video). IAS.
- "Astronomers' doubts about the Dark Side ...". https://www.sciencedaily.com/releases/2010/06/100613212708.htm.
- Gray, Meghan; Merrifield, Mike (2010). "Dark Matter". in Haran, Brady. University of Nottingham. http://www.sixtysymbols.com/videos/darkmatter.htm.
- Carmeli, Oded (27 February 2017). "The physicist who denies that dark matter exists". Cosmos on Nautilus. http://cosmos.nautil.us/short/144/the-physicist-who-denies-that-dark-matter-exists.
Original source: https://en.wikipedia.org/wiki/ Dark matter. Read more