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Dark Matter
Sergio Luigi Cacciatori, Vittorio Gorini, Federico Re
TL;DR
Dark matter remains unidentified and undetected directly despite multiple independent gravitational and cosmological indications of missing mass. The paper surveys astrophysical and cosmological evidence, examines invisible-matter candidates and modified-gravity alternatives, and discusses their strengths and weaknesses. It concludes within this scope that the missing-mass problem remains unresolved, while observations and model tensions continue to challenge aspects of the ΛCDM framework.
Problem
Dark matter has unknown composition, lacks direct detection, and may require a new theory despite many independent indirect evidences.
Method
The paper reviews astrophysical and cosmological evidence, candidate invisible matter such as MACHOs, WIMPs, and axion-like particles, and modified-gravity proposals.
Results
Galaxy rotation curves remain flat at large radii, while cosmological estimates assign about 31.5% to matter and 68.5% to dark energy.
Takeaways & Limitations
The missing-mass problem admits multiple mostly incompatible hypotheses, including invisible matter and modified gravitational dynamics, with no satisfactory solution identified.
Takeaways & Limitations
MOND explains some galactic phenomena but faces difficulties with galaxy-cluster mass, cluster temperature profiles, and globular-cluster velocity dispersions.
Abstract
from arXiv · showhide
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 established physics, whereas dark matter remains unidentified and indirectly inferred from multiple gravitational phenomena. The two should not be conflated.
- Antimatter and dark matter are therefore very different kinds of matter-related concepts.
- Antimatter consists of known antiparticles, such as positrons and antiprotons, with counterparts differing in electric charge.
- Dark matter has no known composition, may require a new theory, and has not been directly detected.
- Despite lacking direct detection, dark matter is supported by independent indirect evidence concerning different phenomena.
2 The many evidences of the dark matter
Dark matter is motivated by several independent observations of gravitational effects, unlike dark energy, whose evidence is described here as more limited. These observations indicate missing gravitational mass, though the supplied passage is truncated.
- The article distinguishes this evidential situation from dark energy, whose existence is tied here to two distinct observations.
- Dark matter is supported by several phenomena and observations, all involving gravitational effects.
- These observations allow estimates of a system’s gravitational attraction and suggest more mass than the visible matter provides.
2.1 Astrophysical evidences for dark matter
Astrophysical evidence for dark matter comes from galaxy dynamics, cluster motions and gas, gravitational lensing, and colliding clusters. Across these systems, gravitational measurements generally exceed what visible matter can explain, though some distributions and exceptions remain uncertain.
- 2.1.1 Galaxy rotation curves: Rotation curves indicate that galaxy gravity exceeds visible-matter gravity, with dark matter concentrated mainly in extended peripheral halos.
- 2.1.1 Galaxy rotation curves: Ultra-diffuse galaxies are a notable exception: some may consist almost entirely of dark matter, while others appear almost entirely free of it.
- 2.1.1 Galaxy rotation curves: Galaxy rotation curves remain flat in outer regions instead of decreasing as expected from visible matter alone, motivating a dark matter halo.
- 2.1.1 Galaxy rotation curves: The Tully-Fisher relation links luminous galaxy mass to flat-region rotation velocity with exponent α ≈ 3.5 ÷ 4, but remains unexplained even within the dark matter paradigm.
- 2.1.2 Virial of clusters: For non-disc systems, virial measurements, gas velocities, and lensing estimate gravitational mass; about 80% may need attribution to invisible matter.
- 2.1.3 X-rays emission from clusters: Cluster X-ray temperatures and gas velocity dispersions imply gravitational masses five or six times larger than observed matter, corresponding to about 80% invisible mass.
- 2.1.4 Gravitational lensing: Gravitational lensing reconstructs lens mass from distorted background images and finds invisible halos five or six times more massive than visible lensing matter.
- 2.1.5 The Bullet Clusters: In Bullet Cluster collisions, lensing mass follows the relatively unimpeded galaxies rather than the slowed hot gas, indicating accompanying dark matter halos.
2.2 Cosmological dark matter evidences
Cosmological observations indicate that visible matter cannot account for the universe’s gravitational content or the formation of its observed structures. The CMB power spectrum further constrains cosmological parameters and supports a nearly flat universe through its acoustic peaks.
- Cosmological matter budget: 31.5% of the universe’s mass-energy content is attributed to matter, while visible matter contributes only about 4.4%, leaving 27.1% as dark matter.The inferred dark-matter share is approximately 86% of total matter.
- Formation of structures: ΛCDM describes structure growth from primordial inhomogeneities through gravitational amplification of overdense and underdense regions.The model predicts a cosmic network of voids, filaments, and walls formed through competing matter and dark-energy effects.
- Formation of structures: Simulations using only visible matter do not produce the present large-scale structures efficiently within the universe’s 13.8-billion-year history.This shortfall motivates additional gravitating matter in the cosmological model.
- CMB evidence: CMB temperature anisotropies, measured by COBE, WMAP, and Planck, preserve imprints of early density inhomogeneities that seeded later cosmic structures.The anisotropies are typically a few tenths of a microkelvin around a mean CMB temperature of 2.73 K.
- CMB evidence: The CMB power spectrum expands temperature correlations into multipoles, with each multipole probing an angular scale of approximately 180°/l.The spectrum is expressed through Legendre-polynomial components and measured in μK2 after travel-related corrections.
- CMB evidence: The first acoustic peak at α≃0.9° combines with the sound-horizon standard ruler to indicate that cosmic space is practically flat.The second peak corresponds to a spherical BAO trough; higher-scale correlations decline because photon diffusion smooths smaller anisotropies.
3 Hypotheses on the missing mass
The paper presents competing hypotheses for the missing-mass problem because no satisfactory solution has yet been established. It emphasizes testing all proposals critically, including the leading hypothesis, against observations.
- No satisfactory solution to the missing-mass problem has been found to date, so the paper treats proposed explanations as hypotheses.
- The hypotheses offer alternative explanations that are mostly mutually incompatible, with some denying dark matter’s existence.
- The paper discusses competing proposals because observations may disprove one, several, or all of them, including the leading hypothesis.
3.1 The Standard Model
The Standard Model organizes known elementary particles and their interactions, describing the constituents from which other physical objects are formed.
- The Standard Model describes the different known classes of elementary particles and their interactions.
- Leptons include neutrinos and their electron, muon, and tau counterparts; each has a corresponding antiparticle.
- Gluons transmit the colour force, while W+, W−, and Z0 are intermediate vector bosons transmitting the weak nuclear force.
- Quarks are spin 1/2 fermions that combine into mesons and baryons because strong interactions prevent their separation.
3.2 Hot dark matter
The paper considers neutrinos as a possible hot-dark-matter candidate because they interact only weakly and gravitationally, but their expected abundance and mass provide too little matter.
- A dark-matter particle hypothesis therefore depends on whether the particles have sizable rest mass or very small mass and whether they move slowly or relativistically.
- If neutrinos possess magnetic moments, their electromagnetic interaction would still be effectively nonexistent because the moments are estimated at 10−19 ∼10−20 times the electron’s.
- Hot dark matter would consist of ultrarelativistic particles forming a very hot gas, requiring either an enormous abundance or relativistic motion.
- Neutrinos appear suitable candidates because they interact only weakly and gravitationally, but their small mass would require an enormous number.
- The Standard Model predicts a neutrino abundance and mass contribution that amount to only a fraction of the visible baryonic mass.
3.3 Cold dark matter: MACHOs
Cold dark matter MACHOs are nonluminous compact bodies whose gravitational effects can be tested through microlensing. Observations constrain their contribution to the Milky Way’s dark-matter halo.
- Cold dark matter refers to invisible bodies moving with subrelativistic velocities; particle candidates would be massive, neutral, and weakly interacting.
- MACHOs are Massive Compact Halo Objects, including isolated black holes, neutron stars, white dwarfs, brown dwarfs, rogue planets, and possibly asteroids.
- Isolated neutron stars that are neither pulsars nor newly formed are not seen and therefore contribute to the missing mass.
- Microlensing occurs when a MACHO passes before a background star or quasar, producing distorted images or magnified light and allowing the lens mass to be calculated.
- Less than a thousand Milky Way microlensing events attributable to MACHOs have been observed, constraining them to no more than 20% of the galaxy’s dark-matter halo.
- Elliptical galaxies may contain a higher MACHO fraction, perhaps up to 50%.
3.4 Cold dark matter: WIMPs
WIMPs are proposed as massive, weakly interacting particles that could constitute cold dark matter, but detecting or producing them requires knowing how they interact with baryonic matter. Experiments remain inconclusive, making the hypothesis increasingly difficult to sustain.
- WIMP proposal: WIMPs are hypothetical massive particles with extremely small interaction cross sections, proposed as cold dark matter because neutrinos are too light.They are expected to interact weakly, while gravitational interactions would be far weaker.
- Detection strategies: Testing WIMPs requires either intercepting them with detectors or creating them in laboratories, but both strategies depend on unknown interactions with baryonic matter.The paper emphasizes that this missing interaction information makes detection and production highly nontrivial.
- Detection strategies: Large quantities of target material may be necessary because weak-interaction cross sections are extremely small.A 200-litre water target contains approximately 6.7 × 10^27 molecules, illustrating the scale required for rare interactions.
- Experimental status: If WIMPs interact only gravitationally, their effective WIMP–nucleon cross section would be no larger than about 10^-70 cm^2, preventing direct collision detection.The paper distinguishes this effective cross section from the infinite range of gravitational forces.
- Experimental status: WIMP searches and production experiments have so far been inconclusive, and experiments testing the neutralino hypothesis concluded that the neutralino does not exist.The paper states that increasingly small inferred production cross sections make accelerator production less plausible.
3.5 Dark matter as axions or axion-like particles?
Axions and axion-like particles are proposed dark-matter candidates connected to symmetry breaking and extremely weak interactions. Their small masses can remain compatible with cold dark matter through bosonic condensation, but their existence remains unproven.
- Axions: The axion was proposed as a neutral, spin-zero particle with mass below 10^-2 eV that couples weakly to matter and addresses the strong CP problem.Its proposal follows from spontaneous symmetry breaking in the relevant theory.
- Axions: Axions can be cold-dark-matter candidates because bosons may form Bose condensates without obeying the Pauli exclusion principle.The paper describes primordial axions cooling into a condensed state that could form dark-matter halos.
- Axions: No proof of axion existence has been obtained, while recent measurements constrain their mass to no more than 10^-6 eV.The paper notes that this mass is too small to have cosmological consequences in the proposed scenario.
- Axion-like particles: ALP fields with masses between 10^-22 eV and 10^-19 eV are proposed to remain out of thermal equilibrium and undergo oscillations followed by fragmentation.The passage connects this parameter range with possible early formation of massive galaxies observed by JWST.
3.6 No dark matter: modified gravity theories
Modified-gravity proposals interpret dark-matter evidence as departures from Newtonian dynamics, with MOND reproducing several galactic patterns but facing broader astrophysical and relativistic challenges.
- The failure to detect dark-matter constituents motivates proposals that large-scale gravitational dynamics deviates from Newtonian laws.
- MOND: The radial acceleration relation compares observed acceleration with the Newtonian acceleration generated by visible baryonic matter.The comparison uses data pairs from different systems to test their relation.
- MOND: At accelerations above approximately 10^-9 metres per square second, observed and baryonic accelerations agree; below it, they diverge approximately as g_obs ≃ √(a_0 g_bar), with a_0 of order 10^-10 metres per square second.
- MOND: MOND modifies Newtonian gravity through an interpolating function that approaches unity at accelerations much larger than a_0 and reproduces the low-acceleration relation.
- MOND: MOND yields a constant peripheral velocity and the baryonic Tully-Fisher relation, in which baryonic mass is proportional to the fourth power of that velocity.
- MOND: MOND’s galactic law is a phenomenological consequence of rotation-curve observations, so its deeper significance requires explaining additional missing-mass evidence.
- MOND: MOND only partially explains galaxy-cluster missing mass and faces difficulties with cluster temperatures, globular-cluster velocity dispersions, and differing ultra-diffuse-galaxy mass contents.
- Relativistic extensions: Relativistic MOND extensions introduce additional fields to recover Newtonian and MOND limits and address cosmological observations, while added parameters can increase model complexity.
3.7 Unexpected effects of general relativity
A minority proposal holds that dark-matter phenomena may arise within general relativity itself, without modifying fundamental gravitational laws, because neglected relativistic effects could matter in complex systems.
- A minority research direction investigates whether general relativity already contains the modifications needed to explain phenomena attributed to dark matter.
- This proposal is motivated by general relativity’s precise confirmation through binary-pulsar observations and gravitational-wave analyses.
- The approach questions simplifying treatments that approximate mass distributions as pointlike or uniformly dense lenses and model cosmic expansion as homogeneous and isotropic.
4 Future perspectives
Future Earth-based and space-based observational programs aim, among other purposes, to clarify the nature and properties of dark matter and dark energy.
- Future ground- and space-based enterprises are being developed to investigate the nature and properties of dark matter and dark energy.