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Dark Matter

Sergio Luigi Cacciatori, Vittorio Gorini, Federico Re

arXiv:2410.10424v1gr-qc

TL;DR

Dark matter’s composition and even its existence remain uncertain despite independent indirect evidence. This article reviews astrophysical and cosmological evidence and surveys invisible-matter and modified-gravity hypotheses; it reports that no satisfactory solution has yet been found.

  • Problem

    Dark matter’s composition and even its existence remain unknown despite independent indirect evidence for it.

    Source: §1.1 · p. 2

  • Method

    The article reviews indirect evidence for dark matter and surveys hypotheses involving invisible matter or modified gravitational dynamics.

    Source: §1.1 · p. 2, §3 · p. 15

  • Results

    No satisfactory solution to the missing-mass problem has been found, and the proposed explanations are mostly mutually incompatible.

    Source: §3 · p. 15

  • Takeaways & Limitations

    The paper uses “missing mass” as a broader framing because some hypotheses deny dark matter and instead posit more complex dynamics.

    Source: §3 · p. 15

    For GIMPs, the effective cross section with nucleons would be no larger than about 10^-70 cm^2, precluding direct detection through collisions.

    Source: §3.4 · p. 26

Abstract

from arXiv · show

In this article we address the mystery of dark matter. We expound the various evidences, astrophysical and cosmological, leading to hypothesize the existence of an invisible form of matter, whose attempts at detecting it have so far all failed. We also discuss some alternative suggestions that replace the hypothesis of exotic matter with the assumption of modifications of the gravitational dynamics. For each of the various proposals we also discuss the strong and weak points.

1 Basic concepts

Antimatter is a well-understood counterpart to ordinary matter, while dark matter remains unidentified and has not been directly detected, despite independent indirect evidence for its existence.

1.1 Dark matter is not antimatter

  • Antimatter is well known and described by the Standard Model, with particles such as positrons serving as counterparts to electrons with opposite electric charge.The positron has the same mass and spin as the electron; the proton and neutron also have corresponding antiparticles.Source: §1.1 · p. 2
  • When matter meets its antimatter counterpart, they annihilate into electromagnetic radiation, a process used to detect gamma rays in PET.The universe contains only a tiny percentage of antimatter compared with ordinary matter.Source: §1.1 · p. 2
  • Dark matter’s composition and even its existence remain unknown, though most scientists believe it exists based on independent indirect evidence despite no direct detection so far.The passage says whether a new theory is needed to describe dark matter is also unknown.Source: §1.1 · p. 2

2 The many evidences of the dark matter

Multiple independent gravitational observations suggest dark matter because visible mass cannot account for measured gravitational acceleration. Explaining one observation differently would not necessarily resolve the others.

2 The many evidences of the dark matter

  • The evidence consists of independent gravitational observations in which visible mass is insufficient to explain a system’s measured gravitational acceleration.These are cases of “missing mass.”Source: §2 · p. 3
  • An alternative explanation for one missing-mass observation would not necessarily explain the others, which could remain unresolved.Source: §2 · p. 3

2.1 Astrophysical evidences for dark matter

Astrophysical evidence for dark matter comes from galactic rotation curves and independent mass estimates for clusters, all indicating more gravitating mass than visible matter alone accounts for.

2.1.1 Galaxy rotation curves

  • Flat outer rotation curves exceed the visible-matter prediction, implying dark matter halos that become important at galactic outskirts and account for about 80% of total mass.The central rotation curve can be explained by visible matter; standard disc galaxies studied so far show similarly shaped halos.Source: §2.1.1 · pp. 4–5, Figure 1 · p. 4
  • The Tully-Fisher relation, M proportional to v_f^α with α about 3.5–4, links luminous mass to flat-region rotation speed and remains unexplained even in the dark matter paradigm.The passage describes the relation as a remarkable coincidence for dark matter accumulation around galaxies.Source: §2.1.1 · p. 5

2.1.2 Virial of clusters

  • Virial estimates of clusters require invisible matter to account for about 80% of their total gravitational mass.For elliptical galaxies, velocity dispersion, external gas velocities, and weak lensing support dark matter, but do not establish whether it forms a halo or mixes with baryonic matter.Source: §2.1.2 · pp. 5–6

2.1.3 X-rays emission from clusters

  • X-ray temperatures imply cluster gas velocities too high for visible mass alone to keep the gas bound, yielding gravitational masses five or six times the observed mass.Source: §2.1.3 · p. 6

2.1.4 Gravitational lensing

  • Gravitational lensing reconstructs mass from distortions of background objects and indicates that lensing systems have invisible halos five or six times more massive than visible matter.Source: §2.1.4 · p. 7

2.1.5 The Bullet Clusters

  • In the Bullet Clusters, lensing places most mass where the colliding clusters are, not their slowed hot gas, indicating that each carried a halo through the collision.The halos are presumed to consist of particles that interact weakly and gravitationally, so they passed through essentially unaltered.Source: §2.1.5 · pp. 7–8

2.2 Cosmological dark matter evidences

Cosmological evidence within ΛCDM indicates that the universe contains substantially more dark matter than visible matter, and that dark matter contributes to the formation of large-scale structure and the CMB’s acoustic-peak pattern.

2.2.1 Fitting the deceleration parameter

  • 31.5% of the universe’s mass content is matter, but only 4.4% of its total mass-energy is normal matter, leaving 27.1% as dark matter.The inferred dark-matter amount is about 86% of total matter, consistent with abundances in galaxies and clusters.Source: §2.2.1 · pp. 8–9

2.2.2 Formation of structures

  • Simulations using visible matter alone do not form today’s structures quickly enough, whereas dark matter halos provide gravity for rapid baryonic infall and subsequent star and galaxy formation.The account traces initial inhomogeneities to quantum fluctuations stretched by inflation; JWST observations of Milky-Way-sized disc galaxies around 400 million years after the Big Bang challenge the early-formation scenario, though rapid star formation in hot, high-pressure halos may explain them [9].Source: §2.2.2 · pp. 10–11

2.2.3 The multipole spectrum of the CMB

  • The CMB’s third acoustic peak independently indicates that dark matter is five to six times more abundant than normal matter, while its first peak’s angular scale supports practically flat spatial curvature.The peak pattern is linked to baryon acoustic oscillations frozen into the CMB at decoupling; the third peak’s amplitude and shape indicate the amount of dark matter in the overdense regions.Source: §2.2.3 · pp. 11, 14, 15

3 Hypotheses on the missing mass

No satisfactory explanation for the missing mass has been found, and the competing hypotheses are mostly incompatible; the preferred hypothesis is invisible matter, but alternatives remain open to observational disproof.

3 Hypotheses on the missing mass

  • The section uses “missing mass” because some hypotheses deny dark matter and instead propose more complex dynamics.The hypotheses are presented as alternative explanations that are mostly mutually incompatible, and no satisfactory solution has been found.Source: §3 · p. 15
  • The invisible-matter hypothesis is currently preferred by most of the scientific community and is discussed first.Source: §3 · pp. 15–16
  • The other hypotheses are considered critically because observations could disprove one or more of them, including the leading hypothesis.Source: §3 · p. 16
  • Visible matter is described using the Standard Model of Elementary Particles, called the Standard Model in the section.Source: §3 · p. 16

3.1 The Standard Model

The Standard Model describes known elementary particles and their interactions. It organizes matter into quarks and leptons and describes the particle forces, except gravity, through interacting quantum fields and force-carrying particles.

3.1 The Standard Model

  • The Standard Model describes known elementary particles and their interactions, with quarks and electrons considered elementary to the best of current knowledge.Protons and neutrons are composed of quarks, while the Standard Model also includes neutrinos, heavier electron-like particles, and the Higgs boson.Source: §3.1 · p. 16
  • Aside from gravity, the weak, electromagnetic, and colour forces are described by quantum fields and transmitted by particles, including photons, gluons, and W+, W−, and Z0 bosons.The colour force has eight gluon types, while the weak force has three intermediate vector bosons.Source: §3.1 · pp. 16–17
  • Quarks are spin-1/2 fermions bound by gluon exchange into mesons or baryons; visible matter is called baryonic because protons and neutrons are baryons.Quarks alone experience the strong interaction; quarks and leptons can interact weakly and electromagnetically, except neutrinos, which interact only weakly. Neutrinos have three types and different masses, but whether all have mass is unknown; the known upper limit is 0.8 eV. Almost all particles are unstable, though protons and neutrons appear stable inside nonradioactive atoms.Source: §3.1 · pp. 16–17

3.2 Hot dark matter

Hot dark matter would consist of very light, relativistic particles, with neutrinos as a possible but quantitatively insufficient candidate. Because such particles cannot account for galactic halos, the evidence described favors dark matter being mostly cold across galactic and cosmological scales.

3.2 Hot dark matter

  • A small-mass dark-matter hypothesis implies either an utterly unimaginable particle abundance or ultrarelativistic particles forming a very hot gas, termed hot dark matter.The text frames the distinction in terms of whether hypothetical particles have sizable or very small rest mass and whether they move slowly or at relativistic speeds.Source: §3.2 · pp. 17–18
  • Neutrinos are plausible hot-dark-matter candidates because they interact only weakly and gravitationally, but their predicted abundance times the upper mass limit yields only a fraction of visible baryonic mass.The Standard Model calculation estimates the number of neutrinos in the visible universe from visible matter and its description of neutrino interactions and generation.Source: §3.2 · p. 18
  • Hot dark matter cannot explain galactic halos because galaxies cannot capture near-light-speed, very light particles; the shared dark-matter abundance across galactic and cosmological scales therefore favors mostly cold matter.The passage says hot dark matter would affect cosmological scales but not galactic ones, implying a stronger cosmological than galactic effect if it were not negligible compared with cold dark matter.Source: §3.2 · p. 18
  • Sterile neutrinos, proposed in grand unification theories, would be right-handed, avoid interaction with baryonic matter, act only gravitationally, and have an abundance uncorrelated with visible matter.Ordinary neutrinos are described as left-handed, with spins antiparallel to their direction of motion; sterile neutrinos would instead have parallel spins.Source: §3.2 · p. 18

3.3 Cold dark matter: MACHOs

Cold dark matter MACHOs are invisible, nonluminous macroscopic bodies proposed as contributors to missing mass. Microlensing observations constrain their contribution in the Milky Way, while primordial black holes remain hypothetical.

3.3 Cold dark matter: MACHOs

  • MACHOs include isolated black holes, neutron stars, white dwarfs, brown dwarfs, rogue planets, and possibly smaller bodies such as wandering asteroids.Rogue planets move freely without orbiting stars, while brown dwarfs are substellar objects that fuse deuterium but not hydrogen; both are effectively invisible.Source: §3.3 · p. 19
  • White dwarfs, neutron stars, and isolated stellar or intermediate-mass black holes can contribute to missing mass because they are compact remnants that may emit no observable radiation.White dwarfs are supported by electron degeneracy pressure and may cool into invisible black dwarfs; neutron stars are supported by neutron degeneracy pressure, and isolated non-pulsars are not seen.Source: §3.3 · pp. 20–21
  • At most 20% of the Milky Way dark matter halo mass is attributable to MACHOs; the figure may reach 50% in elliptical galaxies.Fewer than a thousand MACHO-attributed microlensing events have been observed in the Milky Way; lensing estimates the lens mass from image distortion or magnification.Source: §3.3 · p. 22
  • Primordial black holes, hypothesized to form from early-universe density collapses, would need sufficient mass and low Hawking temperature to persist, but none have been detected to date (2024).They must have had masses of at least 10^11 kg at creation to avoid evaporating by today; a wide mass spectrum would imply some evaporating now, yet none have been observed.Source: §3.3 · p. 22

3.4 Cold dark matter: WIMPs

WIMPs are proposed massive, weakly interacting particles that could constitute cold dark matter, but their properties remain unknown and searches have detected no convincing signal. Failed neutralino searches and increasingly restrictive detection limits have made the hypothesis less plausible.

3.4 Cold dark matter: WIMPs

  • WIMPs are hypothesised massive, neutrino-like particles that interact weakly and could explain observations, but their mass, cross section, and collision products are unknown.Neutrinos were confirmed when predicted photon triplets matched observed rates; unlike that case, WIMP experiments lack a theoretical model to predict interactions.Source: §3.4 · pp. 23, 25
  • A few units times 10^-48 cm^2 is the excluded WIMP-nucleon cross-section scale for reasonable WIMP energies of the order of tens of GeV.Searches use underground cryogenic tanks of liquid scintillators, where a WIMP collision would produce light recorded by photomultipliers; none has detected a WIMP signal.Source: §3.4 · p. 25
  • If detection limits are overcome without a signal, WIMPs would have to interact only gravitationally, with an effective GIMP-nucleon cross section no larger than about 10^-70 cm^2.The paper concludes that such collisions could not be directly detected, leaving dark matter observable only through its gravitational effects on baryonic matter.Source: §3.4 · pp. 25–26
  • Creating WIMPs in accelerators is also uncertain because their mass, production energy, suitable colliding particles, and interaction model are unknown.Particles seen so far in accelerator collisions are unstable and decay rapidly, so they cannot be the WIMPs described here.Source: §3.4 · pp. 26–27
  • Neutralino searches concluded that the neutralino does not exist, and continuing inconclusive WIMP experiments imply production cross sections below those hypothesised so far.The paper says this makes producing enough WIMPs in the Big Bang difficult and the hypothesis increasingly less plausible, though not entirely excluded.Source: §3.4 · p. 28
  • Supersymmetric theories proposed the stable neutralino as a WIMP candidate, and calculations suggested its cross section and abundance could explain dark matter in the “supersymmetric miracle.”The paper says experiments devised to test this hypothesis instead led to the conclusion that the neutralino does not exist.Source: §3.4 · p. 28

3.5 Dark matter as axions or axion-like particles?

The section presents axions and axion-like particles (ALPs) as hypothetical dark-matter candidates, describing proposed mechanisms for their formation and possible evidence from galaxy lensing and early galaxy formation. It also notes that axions could address the strong CP problem, while further lensing examples are needed before drawing definite conclusions about ALPs.

3.5 Dark matter as axions or axion-like particles?

  • A Peccei–Quinn symmetry was proposed to prevent CP violation in strong interactions, and its spontaneous breaking implies a light, weakly coupled neutral particle called the axion.The proposed axion mass is less than 10^-2 eV.Source: §3.5 · pp. 29–30
  • Axions could be cold dark matter because bosons can form a Bose condensate; inflation is proposed to cool primordial axions into halos, while a mass limit of 10^-6 eV does not rule out effects on galaxy dynamics.The text says axions have not been proven to exist and that the mass limit is too small to have cosmological consequences.Source: §3.5 · p. 30
  • ALPs are proposed to form galactic halos as stable solitons through self-interactions, and Primakoff-based searches include ADMX and XENONnT.These experiments seek conversion between photons and axions or ALPs in intense electromagnetic fields.Source: §3.5 · p. 30
  • Lensing distortions in HS 0810-2554 have been interpreted as an ALP wave-soliton interference pattern, with particle masses expected between 10^-22 and 10^-20 eV, seemingly favoring ALP over WIMP halos.The passage says analogous features should be observed in other lensing galaxies before definite conclusions favoring ALPs can be reached.Source: §3.5 · p. 30
  • For ALP masses in the range 10^-22 eV ≲ m_alp ≲ 10^-19 eV, weak interactions may leave the field out of thermal equilibrium, enabling fragmentation into clusters that could seed massive early galaxies [44] [45].The proposed clusters act as potential wells for the formation of massive galaxies observed by JWST.Source: §3.5 · p. 31

3.6 No dark matter: modified gravity theories

This section examines whether modified gravity, including MOND and relativistic alternatives, can explain large-scale dynamics without unseen matter while preserving established small-scale laws, and considers their successes and difficulties. It also notes that precision binary-pulsar measurements have found no deviations from general relativity, refuting many alternative relativistic gravity theories.

3.6.1 MOND

  • Below roughly 10^-9 m/s^2, observed acceleration departs from the baryonic Newtonian prediction toward g_obs ≃ √(a0 g_bar), motivating MOND with a0 = 1.2 × 10^-10 m/s^2.The RAR compares observed acceleration with that predicted from visible baryonic mass; Fig. 4 illustrates the relation for galaxy UGC02487.Source: §3.6.1 · p. 32, Figure 4 · p. 32
  • MOND explains flat galaxy rotation curves and the Tully–Fisher relation, since its low-acceleration law yields constant peripheral velocity and baryonic mass proportional to its fourth power.The section also notes that the ΛCDM model is unable to explain the Tully–Fisher relation.Source: §3.6.1 · p. 32
  • MOND also accounts for the discrepancy–acceleration relation, galaxy surface-brightness cutoffs, high apparent missing mass in some ultra-diffuse galaxies, and Fornax dwarf-galaxy features.Its nonlinear acceleration law also predicts an external field effect, with reported evidence of strong-equivalence-principle violations near rotationally supported galaxies.Source: §3.6.1 · pp. 33–34
  • MOND only partially explains cluster missing mass and faces challenges with cluster temperatures, globular-cluster dispersions, diverse ultra-diffuse galaxies, and Bullet Cluster mass distributions.Proposed responses include unseen non-baryonic mass in clusters and MOND adjustments for some galaxies and Bullet Cluster systems.Source: §3.6.1 · p. 34
  • The cited study concluded that MOND, or any theory behaving similarly at galactic scales, was ruled out as a fundamental theory for galaxies at more than 10σ; this was challenged over uncertain distances and inclinations.Source: §3.6.1 · p. 35
  • Wide-binary analysis found α_grav = -0.021+0.065−0.045, consistent with Newtonian gravity and excluding MOND at 16σ, while earlier studies supported MOND.The dispute remains difficult to resolve because tiny accelerations make the results vulnerable to external disturbances.Source: §3.6.1 · pp. 35–36

3.6.2 Relativistic extensions of MOND and other alternative theories

  • Relativistic extensions include TeVeS, which explains galaxy rotation curves, lensing, expansion, and structure formation but faces CMB and lensing–rotation difficulties; BSTV, STVG, and Skordis–Złośnik models are also described.STVG is reported to account for CMB acoustic peaks, the matter power spectrum, and galaxy-cluster mass profiles; the Skordis–Złośnik proposal reproduces CMB and matter power spectra.Source: §3.6.2 · pp. 36–37
  • Other proposals include F(R), Brans–Dicke, and Verlinde’s entropic gravity, but adding fields and parameters can complicate models and introduce observational inconsistencies.Verlinde’s approach treats gravity as an emergent entropic force and aims to explain missing-mass and dark-energy phenomena without dark matter.Source: §3.6.2 · p. 37
  • No deviations from general relativity have been found using binary-pulsar timing precision, leading to the refutation of many alternative relativistic theories.The passage notes that such theories predict small deviations in binary-system motion, including systems associated with gravitational-wave emissions such as GW170817.Source: §3.6.2 · p. 40

3.7 Unexpected effects of general relativity

A minority proposal holds that effects already present in general relativity, rather than exotic matter or modified gravity, could help explain phenomena attributed to dark matter. The section argues that neglected relativistic effects may matter on large scales, even when Newtonian gravity works locally.

3.7 Unexpected effects of general relativity

  • General relativity’s precision tests in binary pulsars and compact-object merger gravitational waves motivate investigating whether its neglected effects could influence large-scale dynamics despite weak fields and low speeds.Newtonian gravity is considered adequate over small regions, but the passage says relativistic corrections on sufficiently large scales merit investigation.Source: §3.7 · p. 40
  • Simplified general-relativistic treatments use point or uniform-density compact lenses and assume the universe is homogeneous and isotropic at large scales.These assumptions make the equations easier to solve, though their use is not necessarily justified.Source: §3.7 · pp. 40–41
  • Lense–Thirring frame dragging arises from mass currents generating gravitomagnetic fields; though locally small, it may build up across a disc galaxy and partly explain its missing mass.The passage also reports observations of the effect on satellites and gyroscopes orbiting Earth and in binary pulsars.Source: §3.7 · p. 41
  • Because general relativity predicts finite-speed gravity, retarded potentials from changing galaxy masses or distant moving clusters may contribute to dark-matter-content estimates.The passage highlights scales of thousands of light years and greater as potentially relevant.Source: §3.7 · p. 41
  • Identifying the observer relative to coordinate frames in general relativity is a delicate problem that the scientific community has rarely addressed adequately.Source: §3.7 · p. 41

4 Future perspectives

Earth- and space-based telescope projects, active or under construction, aim in part to clarify the nature and properties of dark energy and dark matter.

4 Future perspectives

  • Earth-based telescopes are among the future projects intended to help clarify dark energy and dark matter.The chapter refers readers to Section 4 of the dark energy chapter for descriptions of these projects.Source: §4 · p. 42
  • Space-based telescopes are also among the future projects intended to help clarify dark energy and dark matter.The chapter refers readers to Section 4 of the dark energy chapter for descriptions of these projects.Source: §4 · p. 42
  • The cited telescope projects are active or under construction, and the chapter directs readers to Section 4 of the dark energy chapter for further information.Source: §4 · p. 42
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