Dark Matter

Prerequisites: Cosmology. Full path (17 pages)

Best explanations

Concrete A brief primer on dark matter

Intuitive
Concrete
Abstract
Research
Why is it interesting?

Intuitive

From cosmological observations we know that there must be more mass than we can presently explain through known matter. Hence, there must be something additional that makes up for this mass and this something is called Dark Matter.

Concrete

Several independent observations require more gravitating mass than we see in stars, gas and dust.

Rotation curves. A star on a circular orbit of radius $r$ around the center of a galaxy has speed $v$ given by $v^2/r = G M(r)/r^2$ , where $M(r)$ is the mass inside the orbit. If the mass were concentrated where the light is, then outside the visible disk $M(r)$ would be constant and $v \propto r^{-1/2}$ . Measured rotation curves of spiral galaxies instead stay roughly flat out to large radii, $v \approx \text{const}$ , which requires $M(r) \propto r$ , that is a density falling like $\rho \propto 1/r^2$ in an extended halo.

Galaxy clusters. The velocities of galaxies in clusters, the temperature of the hot X-ray gas and the bending of light from background galaxies (gravitational lensing) all give cluster masses several times larger than the visible mass. In colliding clusters such as the Bullet Cluster, the lensing mass is offset from the hot gas, which carries most of the ordinary mass.

Cosmology. The pattern of temperature fluctuations in the cosmic microwave background and the abundance of light elements from big bang nucleosynthesis fix the density of ordinary (baryonic) matter. The CMB measurements give a physical density of about $\Omega_b h^2 \approx 0.022$ for baryons and $\Omega_c h^2 \approx 0.12$ for dark matter, so dark matter is about $85\%$ of all matter. Without it, the small density fluctuations seen in the CMB would not have had time to grow into the galaxies we see today.

From this evidence, dark matter must be:

non-baryonic and electrically neutral, or at least very weakly coupled to light,
cold or warm, meaning slow enough at the time of structure formation not to wash out small-scale structure,
stable on cosmological time scales,
nearly collisionless and unable to cool by radiating, so that it forms extended halos instead of collapsing into disks.

No particle of the standard model fits. Neutrinos are neutral and stable, but they are too light: their density is $\Omega_\nu h^2 = \sum m_\nu / (93\,\mathrm{eV})$ , which is far below $0.12$ for the allowed masses, and they would be too fast to form galaxies. Popular candidates are weakly interacting massive particles (WIMPs), axions, sterile neutrinos and primordial black holes. An alternative is to modify the law of gravity at small accelerations (MOND), which describes many galaxy rotation curves but has difficulties with clusters and the CMB.

For a nice overview, see this brief primer on Dark Matter.

Abstract

In the standard cosmological model ( $\Lambda$ CDM), cold dark matter enters the Einstein equation as a pressureless perfect fluid, $T^{\mu\nu} = \rho\,u^\mu u^\nu$ , minimally coupled to gravity and to nothing else. In a Friedmann-Lemaître-Robertson-Walker background with scale factor $a(t)$ , conservation of $T^{\mu\nu}$ gives $\rho \propto a^{-3}$ . In linear perturbation theory, inside the horizon and during matter domination, the density contrast $\delta = \delta\rho/\bar\rho$ obeys

$\ddot\delta + 2H\dot\delta = 4\pi G\,\bar\rho\,\delta ,$

whose growing mode is $\delta \propto a$ . Baryons are coupled to photons until recombination and cannot grow before then; dark matter can, which is why it is needed to reach the observed structure.

On galactic scales a collisionless species is described by its phase-space density $f(\vec x,\vec v,t)$ , which obeys the Vlasov-Poisson system

$\partial_t f + \vec v\cdot\nabla_{\vec x} f - \nabla\Phi\cdot\nabla_{\vec v} f = 0, \qquad \nabla^2\Phi = 4\pi G\int f\,d^3v + 4\pi G\rho_{\text{b}} ,$

with $\rho_{\text{b}}$ the baryon density. N-body simulations solve this system and predict the structure of halos.

For a particle species $\chi$ that was once in thermal equilibrium with the standard model plasma, the number density $n$ follows the Boltzmann equation

$\frac{dn}{dt} + 3Hn = -\langle\sigma v\rangle\left(n^2 - n_{\text{eq}}^2\right),$

where $\langle\sigma v\rangle$ is the thermally averaged annihilation cross section. When the annihilation rate $n\langle\sigma v\rangle$ drops below the expansion rate $H$ , the comoving number freezes out. For a cross section that is nearly independent of velocity, this gives approximately

$\Omega_\chi h^2 \approx \frac{3\times10^{-27}\,\mathrm{cm^3\,s^{-1}}}{\langle\sigma v\rangle} .$

A cross section typical of the weak interaction, about $3\times10^{-26}\,\mathrm{cm^3\,s^{-1}}$ , gives $\Omega_\chi h^2 \approx 0.1$ , close to the observed $0.12$ . This coincidence is the "WIMP miracle" referred to in the quote below. Other production mechanisms, such as misalignment for axions or freeze-in for very weakly coupled particles, lead to different relations between couplings and abundance.

The particle mass is bounded from below. For fermions, the Pauli principle limits the phase-space density in halos (Tremaine-Gunn bound), which excludes masses below roughly $0.1$ to $0.5\,\mathrm{keV}$ , depending on the galaxies used. Bosons can be much lighter, down to about $10^{-22}\,\mathrm{eV}$ , where the de Broglie wavelength becomes comparable to the size of small galaxies.

Research

A good way to stay "up-to-date" regarding dark matter research is following http://dmhunters.org

The WIMP miracle is an attractive and fairly generic consequence of the naturalness approach to the Higgs. But, no matter how appealing it is, the WIMP paradigm will have to be replaced, if future experiments give no evidence in support of the idea. How is one to proceed without guidance from the WIMP miracle? An often-used strategy is adding a single elementary particle for the dark matter and, possibly, another particle to mediate a force between the dark and visible sectors. This approach is justified by criteria of “minimality” or “simplicity”. While I agree that, given our ignorance about the dark sector, this is the first thing to try, I also think that the approach, rather than “minimal”, looks awfully shortsighted. We have ample evidence that nature follows a grand scheme. We recognise in the Standard Model features of this grand scheme. Adding one or two particles only for the reason of generating dark matter is not something that nature would do, if she indeed has a grand scheme in mind. It is much more plausible that the dark matter is only the tip of the ice- berg of a sector that serves a structural purpose. This is indeed the logic behind traditional WIMP models. Take the prototypical example of supersymmetry: the WIMP does not come alone, but it is one out of many new particles whose purpose is to stabilise the Higgs mass against quantum corrections. Once we accept that dark matter is unlikely to manifest itself in “minimal” ways, the tree of possibilities grows rapidly. Post-naturalness dark matter could manifest itself in innumerably different manners. Why should dark matter be a single particle charged under a single force, while matter in the universe comes in a variety of states and chemical compounds? Both theoretical activity and experimental searches for dark matter are adapting to this growing number of unconventional and multi-component forms of dark matter. Tension with the predictions of collisionless dark matter at small scales [42] can be relaxed if dark matter is self-interacting [43]. Moreover, dark matter could be much lighter than that expected for a WIMP. The extreme case is the proposal of fuzzy dark matter, made of a particle as light as 10−22 eV [44]. The light dark-matter window, for masses below the GeV range, is not well covered by conventional searches and several new clever techniques have been proposed to explore this region [45]. One of the most appealing aspects of these new ideas is that they are employing techniques borrowed from other sectors of science, from atomic physics to condensed matter. This cross-fertilisation between different research fields is especially needed during a phase of Krisis.

In unconventional models, one cannot exclude the possibility that dark matter is present in the universe in different forms, from dust to compact objects of astronomical size. The detection of gravitational waves [46] has opened a new field of exploration, providing a new tool for probing the existence of compact objects made of exotic matter [47]. These measurements have also revitalised [48] the hypothesis that dark matter is not made by new particles, but by a primordial population of black holes [49]. The field of dark matter is quickly changing and, both on the theoretical and experimental sides, there is growing interest in alternatives to traditional WIMPs. It is likely that the new trend in dark matter will influence the paradigm search during the post-naturalness era and, conversely, that post-natural research will influence dark matter modelling and experimental strategies.

https://arxiv.org/pdf/1710.07663.pdf#page23

The Bullet Cluster as Evidence against Dark Matter by Sabine Hossenfelder

Why is it interesting?

We know from experiments with quite high confidence that there must be something additional to the standard model of particles, which is responsible for quite a large part of the matter in the universe. So far, we don't know what dark matter consists of, because no laboratory experiment on earth was able to detect it. All existing evidence is indirect, from astrophysical and cosmological observations.

See also Five Reasons We Think Dark Matter Exists by Ethan Siegel