nLab dark matter




physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

experiment, measurement, computable physics

Fields and quanta

fields and particles in particle physics

and in the standard model of particle physics:

force field gauge bosons

scalar bosons

matter field fermions (spinors, Dirac fields)

flavors of fundamental fermions in the
standard model of particle physics:
generation of fermions1st generation2nd generation3d generation
quarks (qq)
up-typeup quark (uu)charm quark (cc)top quark (tt)
down-typedown quark (dd)strange quark (ss)bottom quark (bb)
neutralelectron neutrinomuon neutrinotau neutrino
bound states:
mesonslight mesons:
pion (udu d)
ρ-meson (udu d)
ω-meson (udu d)
ϕ-meson (ss¯s \bar s),
kaon, K*-meson (usu s, dsd s)
eta-meson (uu+dd+ssu u + d d + s s)

charmed heavy mesons:
D-meson (uc u c, dcd c, scs c)
J/ψ-meson (cc¯c \bar c)
bottom heavy mesons:
B-meson (qbq b)
ϒ-meson (bb¯b \bar b)
proton (uud)(u u d)
neutron (udd)(u d d)

(also: antiparticles)

effective particles

hadrons (bound states of the above quarks)


in grand unified theory

minimally extended supersymmetric standard model




dark matter candidates


auxiliary fields



The observable universe at large scales seems to behave as if it contains large amount of matter which does have a gravitational effect but does not emit electromagnetic radiation and hence remains “dark” to telescopes. This hypothetical matter is therefore called dark matter.

There are various astronomical observations that suggest the existence of dark matter

  1. galaxy rotation curves – the speed of rotation of galaxies as a function of the distance from their center cannot be explained by the observed visible matter, but an explanation of this dependence by gravitating matter requires the presence of plenty of dark matter;

  2. cosmic microwave background fluctuations – the measured fluctuations in the cosmic microwave background are very well fitted by the standard model of cosmology with cold dark matter (CDM) included. (see also Resonaances, 18 Jan 2013).

  3. Simulations of structure formation in the universe seem to require existence of dark matter in order to reproduce results compatible with observation.

Any further details about the nature of this hypothetical dark matter remain elusive to date. Possible classes of candidates go by various names. For instance “weakly interacting massive particles” (“WIMP”s), hence massive particles that interact via gravity and the weak nuclear force, but not via electromagnetism. Certain neutrino-dark matter scenarios are being discussed (Neutrino White 16) In supersymmetric theories with R-parity imposed, the lightest supersmmetric particle (LSP, such as the gravitino or the neutralino?) is traditionally regarded as a natural candidate for dark matter (EHNOS 84, reviewed in Ellis-Olive 10).

On galactic scales

The cold dark matter paradigm always worked excellently on cosmic scales, while seemingly facing problems with reproducing various observations on the scale of galaxies. But various recent computer simulations (e.g. with FIRE, see the references below) point to these problems all going away when the complex dynamics of star-formation feedback/back-reaction on galactic structure formation (see there for more) is taken into account. We discuss this for:

  1. The cusp-core behaviour

  2. Galactic rotation profiles

  3. Missing satellites

Cusp-core behaviour

Early numerical simulation of dark matter exhibited dark matter halos around galaxies with a sharp density maximum at the center of the galaxy – called a “cusp” in the density profile – while observation on actual galaxies tends to favour a noticeably smoother density distribution at the center – called a “core” of the density profile.

This discrepancy between theory and experiment is (or was) known as the cusp-core problem for dark matter models (see the references below). It is (or was) one of several issues that the dark matter model has (or had) on the scale of galaxies and smaller.

There are two potential resolutions to this problem: a) Either dark matter is more “exotic” than assumed in these simulations, such as being fuzzy dark matter or similar. Or, b), more mundanely, the existing simulations do not properly resolve a subtle effect shown already by more ordinary dark matter.

Recent investigations support possibility b), indicating that the density cusps seen in previous simulations are but an artifact of overly simplified numerical models, and that would-be cusps are diluted and hence smoothed out by bursty star formation leading to dark matter heating (Pontzen-Governato 14, Read-Walker-Steger-18) and/or by dynamical friction in the interstallar medium (ESH 01). See Read 19 for review.

From Justin Read 22 Aug 2018 on Read-Walker-Steger 18:

On large scales, the standard cosmological model (LCDM) gives an excellent description of the cosmic microwave background radiation and the growth of structure. However, on small scales, in our cosmic backyard known as the Local Group, there have been long-standing puzzles. The oldest of these is the “cusp-core” problem. Gas rich dwarf galaxies have much less dark matter (DM) in their inner regions than early numerical models predicted. This could point to more exotic DM models, or to a failure of the cosmological model.

However, there is a simpler solution. The early numerical models, above, considered a universe that contains only DM. Recent models that include gas cooling, star formation, and gas blow-out due to exploding stars find that star formation in dwarfs is bursty.

This bursty star formation occurs due to repeated cycles of gas inflow and outflow. These cause the inner gravitational potential of the dwarf galaxy to fluctuate, kinematically “heating up” the dark matter and lowering its inner density (Pontzen-Governato 14).

A key prediction of such models is that, at a fixed dark matter halo mass, more star formation leads to more dark matter “heating” and, therefore, a lower inner dark matter density, at least in dwarf galaxies. This is the prediction we set out to test in Read-Walker-Steger 18.

Galactic rotation profile

Computer simulation (FIRE) of galactic structure formation using the standard cold dark matter model qualitatively reproduces the peculiar galactic rotation curves that motivated dark matter (or MOND, for that matter) in the first place (Hopkins et al. 17, Figure 4, Figure 5):

graphics grabbed from (Hopkins et al. 17)

and also reproduces well the baryonic Tully-Fisher relation (El-Badry et al. 18, Figure 4) which used to be an issue in the standard cold dark matter model:

graphics grabbed from (El-Badry et al. 18)

More in detail, galaxy rotation curves exhibit a close correlation between angular velocity and total visible enclosed math at any given radius, called the radial acceleration relation (RAR) or mass-discrepancy acceleration relation. This, too, is reproduced in cold dark matter-model (in theoretical physics) computer simulation (Santos-Santos et al. 15, Cintio-Lelli 15, Keller-Wadsley 16, Ludlow et al 16). These early simulations were not found conclusive in Lelli et al 16, section 8.2. But more detailed analysis (PSF 18) and more refined simulation (Dutton-Maccio-Obreja-Buck 19) has then been claimed to confirm the statement.

A conceptual explanation of the mechanism by stellar feedback is discussed in GBFH 19.

Missing satellites?

On the apparent resolution of the missing satellite problem:

Garrison-Kimmel et al. 17, see Garrison-Kimmel 18




A comprehensive review (on 510 pages):

Discussion of possible matter representations that could serve as dark matter:

Discussion of neutrino-dark matter:

  • A White Paper on keV Sterile Neutrino Dark Matter, Journal of Cosmology and Astroparticle Physics, Volume 2017, January 2017 (arXiv:1602.04816)

Issues with defining gravitating mass on non-stationary spacetimes:

A modified gravity theory which is indistinguishable from cold dark matter if the dark matter only interacts with gravity:

  • C. Deffayet, R. P. Woodard, The Price of Abandoning Dark Matter Is Nonlocality (2402.11716v1)


Evidence for dark matter on large cosmic scales is extremely strong, see the above reviews (…). Evidence on smaller scales, starting around the scale of galaxies is problematic, see the above reviews (…). In particular, as yet there is no direct detection of any dark matter particle.


Observational constraints:

Outlook on prospect of direct detection of dark matter:

Argument that dark matter has already be seen across a range of direct detection experiments, but mis-interpreted as noise, due to negligence of the possibility of inelastic plasmon excitations in crystalline solid state detector materials:

  • Noah Kurinsky, Daniel Baxter, Yonatan Kahn, Gordan Krnjaic, A Dark Matter Interpretation of Excesses in Multiple Direct Detection Experiments (arXiv:2002.06937)

  • Yonatan Kahn, from slide 27 on in: Dark matter review, talk at Lake Louise Winter Institute, 2020 (cern:event/846070/contributions/3693217/)

Claimed rebuttal:

  • Alan E. Robinson, Émile Michaud, Comment on A dark matter interpretation of excesses in multiple direct detection experiments [arXiv:2002.06937] (arXiv:2002.08893)

The result of Kurinsky et al. should not be taken as evidence for dark matter, although it does highlight the ongoing need to investigate the effect of collective modes how [sic] we detect radiation.


  • Noah Kurinsky, Daniel Baxter, Yonatan Kahn, Gordan Krnjaic, Peter Abbamonte, Reply to Robinson and Michaud, arXiv:2002.08893 (arXiv:2003.00101)

the points raised by RM do not invalidate our primary conclusions, as they pertain to a much different energy scale than we discuss in our paper.

Core-cusp problem

  • Amr El-Zant, Isaac Shlosman, Yehuda Hoffman, Dark Halos: The Flattening of the Density Cusp by Dynamical Friction, The Astrophysical Journal, Volume 560, Number 2 (arXiv:astro-ph/0103386)

  • Andrew Pontzen, Fabio Governato, Cold dark matter heats up, Nature, 506, 171 - 178 (13 Feb 2014) (arXiv:1402.1764)

  • Jose Oñorbe, Michael Boylan-Kolchin, James S. Bullock, Philip F. Hopkins, Dušan Kerěs, Claude-André Faucher-Giguère, Eliot Quataert, Norman Murray, Forged in FIRE: cusps, cores, and baryons in low-mass dwarf galaxies, Monthly Notices of the Royal Astronomical Society, Volume 454, Issue 2, 1 December 2015 (arXiv:1502.02036)

  • Justin Read, O. Agertz, M. L. M. Collins, Dark matter cores all the way down, Monthly Notices of the Royal Astronomical Society, Volume 459, Issue 3, 1 July 2016 (arXiv:1508.04143)

  • Justin Read, M. G. Walker, P. Steger, Dark matter heats up in dwarf galaxies, Monthly Notices of the Royal Astronomical Society (arXiv:1808.06634, doi:10.1093/mnras/sty3404, talk recording, press release)

  • Justin Read, Dark matter heats up in dwarf galaxies, Simons Foundation Lecture 2019

  • Matthew D. A. Orkney, Justin Read, et al., EDGE: Two routes to dark matter core formation in ultra-faint dwarfs (arXiv:2101.02688)

See also

Computer simulation

Discussion of computer simulation of dark matter structure formation on galaxy-scales:

  • Hopkins et al. FIRE-2 Simulations: Physics versus Numerics in Galaxy Formation. Monthly Notices of the Royal Astronomical Society, Volume 480, Issue 1, 11 October 2018, Pages 800–863 (arXiv:1702.06148, doi:10.1093/mnras/sty1690)

  • El-Badry et al. Gas Kinematics in FIRE Simulated Galaxies Compared to Spatially Unresolved HI Observations, Monthly Notices of the Royal Astronomical Society, Volume 477, Issue 2, 21 June 2018, Pages 1536–1548 (arXiv:1801.03933, doi:10.1093/mnras/sty730)

  • Shea Garrison-Kimmel et al. Not so lumpy after all: modeling the depletion of dark matter subhalos by Milky Way-like galaxies (arXiv:1701.03792)

  • Shea Garrison-Kimmel, Next-generation Galaxy Formation Simulations with FIRE, 2018 (video recording)

See also

  • Jie Wang, Sownak Bose, Carlos S. Frenk, Liang Gao, Adrian Jenkins, Volker Springel, Simon D. M. White, Universality in the structure of dark matter haloes over twenty orders of magnitude in halo mass (arXiv:1911.09720)

Galaxy rotation curves

On the radial acceleration relation:

  • Arianna Di Cintio, Federico Lelli, The mass discrepancy acceleration relation in a ΛCDM\Lambda CDM context, Monthly Notices of the Royal Astronomical Society: Letters, Volume 456, Issue 1, 11 February 2016, Pages L127–L131 (arXiv:1511.06616, doi:10.1093/mnrasl/slv185)

  • Isabel M. Santos-Santos et al. The distribution of mass components in simulated disc galaxies (arXiv:1510.02474)

  • B.W. Keller, J.W. Wadsley, ΛCDM\Lambda CDM is Consistent with SPARC Radial Acceleration Relation (arXiv:1610.06183)

  • Aaron D. Ludlow et. al. The Mass-Discrepancy Acceleration Relation: a Natural Outcome of Galaxy Formation in Cold Dark Matter halos, Phys. Rev. Lett. 118, 161103 (2017) (arXiv:1610.07663)

  • Chiara Di Paolo, Paolo Salucci, Jean Philippe Fontaine, The Radial Acceleration Relation (RAR): the crucial cases of Dwarf Discs and of Low Surface Brightness galaxies, ApJ 2019 (arXiv:1810.08472)

  • Chiara Di Paolo, Paolo Salucci, Jean Philippe Fontaine, The Radial Acceleration Relation (RAR): the crucial cases of Dwarf Discs and of Low Surface Brightness galaxies, ApJ 2019 (arXiv:1810.08472)

  • Aaron A. Dutton, Andrea V. Macciò, Aura Obreja, Tobias Buck, NIHAO XVIII: Origin of the MOND phenomenology of galactic rotation curves in a LCDM universe (arXiv:1902.06751)

Critical comments in

  • Federico Lelli, Stacy S. McGaugh, James M. Schombert, Marcel S. Pawlowski, section 8.2 of One Law To Rule Them All: The Radial Acceleration Relation of Galaxies (arXiv:1610.08981)

Conceptual explanation by stellar feedback:

  • Michael Y. Grudić, Michael Boylan-Kolchin, Claude-André Faucher-Giguère, Philip Hopkins, Stellar feedback sets the universal acceleration scale in galaxies (arxiv:1910.06345)


The observation that the “invisible axion” is a candidate for dark matter is due to three groups:

  • John Preskill, M. Wise, Frank Wilcek, Cosmology of the invisible axion, Phys. Lett. B 120:127-32 (1983)

  • L.F. Abbott, P. Sikivie, A Cosmological Bound on the Invisible Axion, Phys.Lett. B120:133-36 (1983)

  • Michael Dine, Willy Fischler, The Not So Harmless Axion, Phys.Lett. B120:137-141 (1983)

A proposal that axions account for fuzzy dark matter, and thus fix the WIMP model for dark matter with its problem of reproducing galactic rotation curves, is in

  • Lam Hui, Jeremiah P. Ostriker, Scott Tremaine, Edward Witten, On the hypothesis that cosmological dark matter is composed of ultra-light bosons, Phys. Rev. D 95, 043541 (2017) (arXiv:1610.08297)

Discussion in the broader context of Kalb-Ramond fields:

  • Christian Capanelli, Leah Jenks, Edward W. Kolb, Evan McDonough, Cosmological Implications of Kalb-Ramond-Like-Particles [arXiv:2309.02485]

Lightest super-partner

The observation that the lightest supersymmetric particle would be a natural dark matter candidate goes back to

  • John Ellis, J.S. Hagelin, Dimitri V. Nanopoulos, Keith Olive, M. Srednicki Supersymmetric relics from the Big Bang, Nuclear Physics B 238[2]: 453-76, 1984 (SPIRE)

with review in


On the gravitino as a dark matter candidate:

A proposal for super-heavy gravitinos as dark matter, by embedding D=4 N=8 supergravity into E10-U-duality-invariant M-theory:

following the proposal towards the end of

  • Murray Gell-Mann, introductory talk at Shelter Island II, 1983 (pdf)

    in: Shelter Island II: Proceedings of the 1983 Shelter Island Conference on Quantum Field Theory and the Fundamental Problems of Physics. MIT Press. pp. 301–343. ISBN 0-262-10031-2.

Further discussion:

Last revised on June 5, 2024 at 19:43:00. See the history of this page for a list of all contributions to it.