Modified Gravity and Cosmology

Many aspects of the large-scale structure of the Universe can be described successfully using cosmological models in which $27\ifmmode\pm\else\textpm\fi{}1%$ of the critical mass-energy density consists of cold dark matter (CDM). However, few---if any---of the predictions of CDM models have been successful on scales of $\ensuremath{\sim}10\text{ }\text{ }\mathrm{kpc}$ or less. This lack of success is usually explained by the difficulty of modeling baryonic physics (star formation, supernova and black-hole feedback, etc.). An intriguing alternative to CDM is that the dark matter is an extremely light ($m\ensuremath{\sim}{10}^{\ensuremath{-}22}\text{ }\text{ }\mathrm{eV}$) boson having a de Broglie wavelength $\ensuremath{\lambda}\ensuremath{\sim}1\text{ }\text{ }\mathrm{kpc}$, often called fuzzy dark matter (FDM). We describe the arguments from particle physics that motivate FDM, review previous work on its astrophysical signatures, and analyze several unexplored aspects of its behavior. In particular, (i) FDM halos or subhalos smaller than about $1{0}^{7}(m/{10}^{\ensuremath{-}22}\text{ }\text{ }\mathrm{eV}{)}^{\ensuremath{-}3/2}$ ${M}_{\ensuremath{\bigodot}}$ do not form, and the abundance of halos smaller than a few times $1{0}^{10}(m/{10}^{\ensuremath{-}22}\text{ }\text{ }\mathrm{eV}{)}^{\ensuremath{-}4/3}$ ${M}_{\ensuremath{\bigodot}}$ is substantially smaller in FDM than in CDM. (ii) FDM halos are comprised of a central core that is a stationary, minimum-energy solution of the Schr\"odinger-Poisson equation, sometimes called a ``soliton,'' surrounded by an envelope that resembles a CDM halo. The soliton can produce a distinct signature in the rotation curves of FDM-dominated systems. (iii) The transition between soliton and envelope is determined by a relaxation process analogous to two-body relaxation in gravitating N-body systems, which proceeds as if the halo were composed of particles with mass $\ensuremath{\sim}\ensuremath{\rho}{\ensuremath{\lambda}}^{3}$ where $\ensuremath{\rho}$ is the halo density. (iv) Relaxation may have substantial effects on the stellar disk and bulge in the inner parts of disk galaxies, but has negligible effect on disk thickening or globular cluster disruption near the solar radius. (v) Relaxation can produce FDM disks but a FDM disk in the solar neighborhood must have a half-thickness of at least $\ensuremath{\sim}300(m/{10}^{\ensuremath{-}22}\text{ }\text{ }\mathrm{eV}{)}^{\ensuremath{-}2/3}\text{ }\text{ }\mathrm{pc}$ and a midplane density less than $0.2(m/{10}^{\ensuremath{-}22}\text{ }\text{ }\mathrm{eV}{)}^{2/3}$ times the baryonic disk density. (vi) Solitonic FDM subhalos evaporate by tunneling through the tidal radius and this limits the minimum subhalo mass inside $\ensuremath{\sim}30\text{ }\text{ }\mathrm{kpc}$ of the Milky Way to a few times $1{0}^{8}(m/{10}^{\ensuremath{-}22}\text{ }\text{ }\mathrm{eV}{)}^{\ensuremath{-}3/2}$ ${M}_{\ensuremath{\bigodot}}$. (vii) If the dark matter in the Fornax dwarf galaxy is composed of CDM, most of the globular clusters observed in that galaxy should have long ago spiraled to its center, and this problem is resolved if the dark matter is FDM. (viii) FDM delays galaxy formation relative to CDM but its galaxy-formation history is consistent with current observations of high-redshift galaxies and the late reionization observed by Planck. If the dark matter is composed of FDM, most observations favor a particle mass $\ensuremath{\gtrsim}{10}^{\ensuremath{-}22}\text{ }\text{ }\mathrm{eV}$ and the most significant observational consequences occur if the mass is in the range $1--10\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}22}\text{ }\text{ }\mathrm{eV}$. There is tension with observations of the Lyman-$\ensuremath{\alpha}$ forest, which favor $m\ensuremath{\gtrsim}10--20\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}22}\text{ }\text{ }\mathrm{eV}$ and we discuss whether more sophisticated models of reionization may resolve this tension.

Ultralight scalars as cosmological dark matter

A wealth of astronomical data indicate the presence of mass discrepancies in the Universe. The motions observed in a variety of classes of extragalactic systems exceed what can be explained by the mass visible in stars and gas. Either (i) there is a vast amount of unseen mass in some novel form — dark matter — or (ii) the data indicate a breakdown of our understanding of dynamics on the relevant scales, or (iii) both. Here, we first review a few outstanding challenges for the dark matter interpretation of mass discrepancies in galaxies, purely based on observations and independently of any alternative theoretical framework. We then show that many of these puzzling observations are predicted by one single relation — Milgrom’s law — involving an acceleration constant a0 (or a characteristic surface density Σ† = a0/G) on the order of the square-root of the cosmological constant in natural units. This relation can at present most easily be interpreted as the effect of a single universal force law resulting from a modification of Newtonian dynamics (MOND) on galactic scales. We exhaustively review the current observational successes and problems of this alternative paradigm at all astrophysical scales, and summarize the various theoretical attempts (TeVeS, GEA, BIMOND, and others) made to effectively embed this modification of Newtonian dynamics within a relativistic theory of gravity.

Modified Newtonian Dynamics (MOND):Observational Phenomenology and Relativistic Extensions

We use cosmological simulations to study the effects of self-interacting dark matter (SIDM) on the density profiles and substructure counts of dark matte r halos from the scales of spiral galaxies to galaxy clusters, focusing explicitly on mod els with cross sections over dark matter particle mass σ/m = 1 and 0.1 cm 2 /g. Our simulations rely on a new SIDM N-body algorithm that is derived self-consistently from the Boltz mann equation and that reproduces analytic expectations in controlled numerical experiments. We find that well-resolved SIDM halos have constant-density cores, with significantly lowe r central densities than their CDM counterparts. In contrast, the subhalo content of SIDM halos is only modestly reduced compared to CDM, with the suppression greatest for large hosts and small halo-centric distances. Moreover, the large-scale clustering and halo circular vel ocity functions in SIDM are effectively identical to CDM, meaning that all of the large-scale successes of CDM are equally well matched by SIDM. From our largest cross section runs we are able to extract scaling relations for core sizes and central densities over a range o f halo sizes and find a strong correlation between the core radius of an SIDM halo and the NFW scale radius of its CDM counterpart. We construct a simple analytic model, based on CDM scaling relations, that captures all aspects of the scaling relations for SIDM halos. Our results show that halo core densities in σ/m = 1 cm 2 /g models are too low to match observations of galaxy clusters, low surface brightness spirals (LSBs), and dwarf spheroidal galaxies. However, SIDM with σ/m ≃ 0.1 cm 2 /g appears capable of reproducing reported core sizes and central densities of dwarfs, LSBs, and galaxy clusters without the need for velocity dependence. Higher resolution simulations over a wider range of masses will be required to confirm this expectation. We discuss constraints arising from the Bullet cluster observ ations, measurements of dark matter density on small-scales and subhalo survival requirements, and show that SIDM models with σ/m ≃ 0.1 cm 2 /g ≃ 0.2 barn/GeV are consistent with all observational constraints.

Cosmological Simulations with Self-Interacting Dark Matter I: Constant Density Cores and Substructure

Dark Matter Self-interactions and Small Scale Structure

This paper gives an overview of the attempts to determine the distribution of dark matter in low surface
brightness disk and gas-rich dwarf galaxies, both through observations and computer simulations. Observations
seem to indicate an approximately constant dark matter density in the inner parts of galaxies, while
cosmological computer simulations indicate a steep power-law-like behaviour. This difference has become
known as the “core/cusp problem,” and it remains one of the unsolved problems in small-scale cosmology.

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de Blok

Papers

The Core-Cusp Problem