2. DARK MATTER

Over the last thirty years, a mountain of evidence has accumulated indicating that the bulk of the matter in the Universe is dark. Observations of galaxies and galaxy clusters reveal substantially more mass associated with these systems than can be attributed to the luminous matter. The evidence includes flat spiral galaxy rotation curves, dynamical studies of satellite galaxies, galaxy-galaxy lensing, dynamical, X-ray, weak lensing, and Sunyaev Zel'dovich (SZ) studies of galaxy clusters, and the large-scale peculiar motions of galaxies. Taken together, these observations have consistently pointed to a matter density, expressed as a fraction of the critical density for a flat Universe, of _m 0.15 - 0.3. In addition, recent measurements of the cosmic microwave background (CMB) anisotropy, of the cosmic shear (large-scale weak lensing), of the galaxy and Lyman-alpha forest clustering power spectra, and of the galaxy cluster abundance have provided independent and consistent estimates of the cosmic mass density (in the context of additional assumptions about the formation of structure in the Universe and in combination with measurements of the Hubble parameter), yielding _m 0.3 (for recent reviews, see, e.g., [Primack(2000), Turner(2001)]).

The bulk of the dark matter in the Universe must be non-baryonic. Estimates of the cosmic baryon density, traditionally from big bang nucleosynthesis (e.g., [Burles et al.(2001)]) and more recently from the CMB anisotropy [Pryke et al.(2001), Netterfield et al.(2001), Stompor et al.(2001)], now yield _b h² = 0.02; combined with measurement of the Hubble parameter (h = 0.72 ± 0.07 from the HST Key Project [Freedman et al.(2001)]), this implies _b 0.04, substantially below the total matter density. The case for non-baryonic dark matter has been strengthened by independent measurements of _m / _b 7 - 9, from the cluster baryon fraction (SZ and X-ray measurements) and from preliminary detection of baryonic wiggles in the large-scale power spectrum [Percival et al.(2001), Miller et al.(2001)]. In addition, the fact that _b > _Luminous 0.007 argues that a substantial fraction of the baryons in the Universe are also dark (perhaps in the form of compact objects or MACHOs).

Since the pattern of CMB anisotropy indicates that the spatial geometry of the universe is nearly flat, _tot 1 [Pryke et al.(2001), Netterfield et al.(2001), Stompor et al.(2001)], the Universe must be dominated by a component - the so-called Dark Energy - which is smoothly distributed on at least the scale of clusters. In order for this component not to have disrupted the formation of structure, it should have come to dominate the energy density only at quite recent epochs, which implies that its effective pressure should be negative. This is consistent with observations of the apparent brightness of high-redshift SNe Ia, which indicate directly the presence of dark energy accelerating the Universe [Perlmutter et al.(1999a), Riess et al.(1998a)]. A consistent cosmological model has thus emerged, in which _m 0.3 and _de 0.7.

While the observational evidence for dark matter and dark energy has been building, we still have no solid clues as to the identities of either of these two components. Nevertheless, their mere existence strongly points to physics beyond (perhaps way beyond) the standard model. Experiments aimed at trying to discover the nature of the dark matter and the dark energy are therefore critical for progress in both particle physics and cosmology. For the remainder of this section, we focus on recent developments in understanding the role of dark matter; the following section describes dark energy.

As has often been pointed out, the uncertainty in the mass of the (non-baryonic) dark matter constituent ranges over at least 70 orders of magnitude, from ~ 10^-5 eV (for axions) to ~ 10⁶³ eV (for planetary mass primordial black holes). Within this vast range, the theory of structure formation provides indirect evidence about some of the properties which the (bulk of the) dark matter must have (see below).

From the theoretical perspective, particle physics theories beyond the standard model do provide well-motivated candidates for non-baryonic dark matter. In supersymmetric models with conserved R-parity, the lightest supersymmetric partner (LSP) of ordinary fermions and bosons is stable. Such a particle is weakly interacting and has a mass of order the electroweak scale (hence the moniker WIMP, for weakly interacting massive particle); in combination, these properties imply that the LSP should have a relic cosmic density of order _m ~ 1 (within a few orders of magnitude) [Jungman et al.(1996)]. The axion, a stable pseudo-Nambu-Goldstone boson which emerges from models which address the strong CP problem via a global U(1) (Peccei-Quinn) symmetry, is also constrained by astrophysical and cosmological arguments to have a density of order the critical density, if it exists.

The SUSY LSP and the axion are both plausible candidates for cold dark matter, with similar effects on the growth of large-scale structure, but their experimental signatures are quite different [Sadoulet(2000)]. Direct searches for WIMPs in the halo of the Galaxy are now becoming mature--relying on the deposition of ~ keV of recoil energy when a WIMP scatters from a nucleus in a detector. Several experiments have reported bounds on WIMP masses and cross-sections [Abusaidi et al.(2000), Baudis et al.(2001)], with one controversial report of a detection via the annual modulation signal [Bernabei et al.(2000)]. The challenge for the next generation of direct detection experiments is to scale up the detector mass while continuing to beat down systematic backgrounds, in order to achieve sensitivity to much smaller event rates and thereby probe a large swath of SUSY parameter space. In addition, indirect WIMP searches, which rely on detection of high-energy gamma rays or charged particles from WIMP annihilation in the halo, or high-energy neutrinos from annihilations in the Earth or the Sun, will gain sensitivity with the coming round of large experiments such as GLAST, VERITAS, and ICECUBE. These direct and indirect WIMP searches should be considered complementary to searches for supersymmetry at colliders. Axion searches involve the resonant conversion of halo axions into microwave photons in the presence of a strong magnetic field; several experiments around the world are underway and are also planning upgrades which should enable them to probe the range of axion masses and couplings expected from theory [Asztalos et al.(2001a), Asztalos et al.(2001b)]. Both direct and indirect searches for particle dark matter are sensitive to some degree to the phase space distribution of dark matter particles in the Galaxy halo. Recent N-body simulations of cold dark matter have stimulated investigations of the expected clumpy nature of halo dark matter and its possible implications for experimental signatures [Blasi and Sheth(2000), Stiff et al.(2001), Moore et al.(2001), Calcaneo-Roldan and Moore(2000)].

In assessing dark matter candidates, we should continue to be cognizant of possible surprises and therefore keep an open mind: theory has provided a multitude of possible candidates beyond WIMPs and axions and could provide new ones. The experiments above are rightly aimed at what are currently considered the most plausible theoretical candidates, but some thought should go into constraining other possibilities.

Models of structure formation provide important clues about the nature of the dark matter, strongly suggesting that the bulk of it is (at most) weakly interacting and non-relativistic at late times (cold dark matter, CDM). Measurements of the CMB anisotropy on degree scales and larger indicate that the inflationary paradigm with nearly scale-invariant, adiabatic perturbations is a very strong candidate for the origin of structure. As noted above, in the context of this paradigm, measurements of galaxy and mass clustering from galaxy surveys point to a model with _m 0.3 in a dark matter component which can freely cluster on scales larger than of order a few kpc. On the other hand, as cosmological N-body simulations of structure formation have pushed to resolve smaller scales, they have uncovered potential discrepancies between CDM models, in which the dark matter is assumed cold (non-relativistic) and collisionless (weakly interacting with itself and with baryons and photons), and the observed properties of galaxy halos. In particular, CDM models predict dark matter halos with steep, `cuspy' inner density profiles, (r) ~ r^-n, with n 1 - 1.5, while rotation curves for dwarf and low surface brightness (LSB) galaxies indicate constant density cores (e.g., [Flores and Primack(1994), Moore(1994), Navarro et al.(1996), Moore et al.(1999a), Jing and Suto(2000), Klypin et al.(2001)]). In addition, these simulations predict that the Local Group of galaxies should include substantially more dwarf satellite galaxies than are observed [Kauffmann et al.(1993), Moore et al.(1999b), Klypin et al.(1999)]: CDM halos appear to have too much surviving substructure.

The cusp and substructure problems (among others [Sellwood and Kosowsky(2000)]) have prompted a number of authors to recently (re-)consider scenarios in which the fundamental properties of the dark matter are modified. In these alternatives, one no longer assumes that (all) the dark matter is both cold and collisionless: it has a new property which suppresses its small-scale clustering, thereby causing halos to be less cuspy and lumpy. Examples include dark matter which self-interacts [Spergel and Steinhardt(2000), Goodman(2000), Peebles(2000)], annihilates [Riotto and Tkachev(2000), Kaplinghat et al.(2000)], decays [Cen(2001)], has a non-negligible Compton wavelength (fuzzy dark matter) [Hu et al.(2000)], or has a non-negligible velocity dispersion (warm dark matter) [Colombi et al.(1996), Sommer-Larsen and Dolgov(2001), Bode et al.(2001)]. Another possibility is to stick with cold, collisionless dark matter but suppress the primordial power spectrum on small length scales [Kamionkowski and Liddle(2000), White and Croft(2000)].

The degree to which these different alternatives solve the difficulties of `oridinary' cold dark matter has been somewhat controversial [Yoshida et al.(2000), Miralda-Escude(2000), Davé et al.(2001), Dalcanton and Hogan(2000), Kochanek and White(2000)]. From the theoretical standpoint, the proposed new dark matter properties are not particularly attractive. For example, warm dark matter requires a stable particle with a mass of order 1 keV, not particularly close to the electroweak or SUSY scale, which must decouple before a significant amount of entropy is transferred to the CMB, so that its cosmic abundance can be suppressed. For annihilating dark matter, one must suppress catastrophic annihilations in the early universe. For self-interacting dark matter, one must supply a new interaction with the requisite strength. The case for `non-standard' dark matter properties would certainly be more appealing if they could be shown to arise naturally in the context of compelling extensions of the standard model of particle physics; while some work has been done along these lines (e.g., [Bento et al.(2000), Sommer-Larsen and Dolgov(2001)]), this remains a challenge for model-builders.

It should also be noted that there may be more pedestrian `astrophysical' explanations for these discrepancies, involving either the data or the fact that the simulations include only a limited physical description of the baryons. For example, new and reanalyzed data on the rotation curves of dwarf and LSB galaxies, with allowance made for beam-smearing effects, has led some authors to conclude that these systems do not discriminate strongly between constant density and cuspy inner halos [van den Bosch et al.(2000), van den Bosch and Swaters(2001), Swaters(2001)]; however, another recent study has found that LSB rotation curves are definitely not well fit by cuspy cores [de Blok et al.(2001)]. It has also been suggested that the interactions of supermassive black holes (now known to be ubiquitous in the cores of galaxies) could destroy dark matter cusps when young galaxies merge [Merritt and Cruz(2001)]. In addition, the overabundance of galactic satellites may be reduced by reionization, which suppresses gas accretion and thus star formation in these low-mass clumps [Bullock et al.(2000)]. In this picture, the observed lack of halo substructure may be a property of the stellar baryons but not of the dark matter. Finally, it has been suggested that both the cusp and substructure problems could be resolved by the effects of galactic winds [Binney et al.(2001)].

More data on the structure of halos and improved modeling of them is needed to ultimately resolve whether observed galaxy halos are consistent with `ordinary' cold dark matter. Nevertheless, the study of alternative dark matter properties that the cusp and substructure problems stimulated remains of interest, because the issue can be turned around: we can use structure formation to constrain the properties of dark matter [Hogan and Dalcanton(2000)]. For example, for warm dark matter (WDM), the high phase space density of dwarf spheroidal galaxies implies a lower limit on the WDM particle mass, m_X > 0.7 keV [Dalcanton and Hogan(2000)]. The observed opacity distribution of the Lyman-alpha forest at redshift z ~ 3 leads to a similar lower mass limit [Narayanan et al.(2000)]. Requiring that sufficiently massive black holes be able to form in time to power the observed highest redshift quasars at z ~ 6 and that high-redshift galaxies be able to reionize the Universe by that epoch also lead to qualitatively similar bounds [Barkana et al.(2001)]. On the other hand, if the WDM mass is much above 1 keV, it will only suppress power on mass scales well below 10¹⁰ M and therefore lead to structure on galaxy scales that is indistinguishable from CDM. Further data on halo structure, e.g., from strong gravitational lensing [Keeton(2001), Keeton and Madau(2001)] and from galaxy-galaxy lensing, and on halo clustering and abundances at high redshift will help constrain the nature of the dark matter. (For example, self-interacting dark matter models generally predict that galaxy halos are spherical instead of elliptical; in principle, the shapes of halos can be probed by lensing, by the dynamics of halo tracers in the Galaxy, by polar ring galaxies, and by X-rays from massive galaxies, among other methods.)

Large-scale structure can also place useful constraints on the masses of particles which contribute only a small fraction of the dark matter density - neutrinos. The atmospheric neutrino data from Super-Kamiokande and MACRO, interpreted as an effect of neutrino oscillations, indicate a neutrino mass squared difference of order m² (2 - 6) × 10^-3 eV², which implies a lower bound on the neutrino cosmic density of > 0.0008. On the other hand, the observed clustering of galaxies and the Lyman- forest implies an upper bound on : since neutrinos are relativistic until late times, they free-stream out of perturbations on small scales, thereby damping small-scale power if they make an appreciable contribution to _m. The current observations translate into the (roughly 2) upper limit m < 3 eV for the combined masses of light stable neutrinos [Croft et al.(1999), Wang et al.(2001)], comparable to current experimental limits on m_e from tritium experiments. In the near future, neutrino masses as low as m ~ 0.3 eV can be probed by combining CMB experiments (MAP and Planck) with galaxy and Lyman- forest power spectrum data from the Sloan Digital Sky Survey [Hu et al.(1998)]. These improved constraints are again comparable to expected improvements in the experimental bounds on m_e.

Partly motivated by the perceived problems of `ordinary' cold dark matter noted above, there has been renewed attention paid to alternatives to dark matter: the mass discrepancies in galaxies normally ascribed to dark matter could instead be signalling the breakdown of Newtonian gravity (for a recent review, see, e.g., [Sellwood and Kosowsky(2000)]). Until the dark matter is actually detected, this may remain a logical possibility. The most commonly discussed alternative, modified Newtonian dynamics (MOND) [Milgrom(1983a)], may be expressed as a modification of the law of inertia below some fundamental acceleration scale; with an appropriate modification, the observed flat rotation curves of galaxies can be reproduced [Milgrom(1983b)]. The degree to which MOND is consistent with the range of astrophysical data continues to be debated. Moreover, the fact that MOND is only a phenomenological prescription for describing dynamical systems, not a fundamental theory, has hampered attempts to apply it to cosmology [Scott et al.(2001)], structure formation, and gravitational lensing [Mortlock and Turner(2001)].

While it is important to keep an open mind to dark matter alternatives, it is also necessary to subject them to observational tests and to hold them up to the lamp of theoretical plausibility. When MOND was first proposed, in the early 1980's, galaxy rotation curves offered the primary evidence for a mass discrepancy, and MOND was aimed at providing an alternative explanation for these observations. Although rotation curves still provide the strongest evidence for a mass discrepancy, ancillary circumstantial evidence for dark matter has built up substantially in the intervening years. As noted at the beginning of this Section, this newer evidence is of two kinds: (a) direct inference of mass discrepancies in galaxies and clusters using a variety of probes, and (b) consistency of the cold dark matter model with _m 0.3 with CMB, SNe Ia, large-scale structure, and weak lensing data. Although MOND cannot address most of these other observations without being embedded in a fundamental theory, as these new pieces of evidence mount up the possibility of explaining them all with something other than dark matter becomes less likely. On the theoretical side, while particle physics theory provides well-motivated candidates for cold dark matter, it has proved difficult to embed MOND in a more fundamental theory; part of this difficulty likely traces to the fact that it appears to violate cherished principles such as the equivalence principle, Lorentz invariance, and conservation of momentum [Scott et al.(2001)Scott, White, Cohn, and Pierpaoli]. Again, if it could be shown that dark matter alternatives arise naturally from new ideas in particle physics or gravitation, the case would be substantially more compelling (for some attempts, see, e.g., [Kinney and Brisudova(2000), Mannheim and Kazanas(1989)]). Finally, it should be noted that modified gravity could in principle be falsified (along with self-interacting dark matter) by better data on the shapes of `dark' halos or by confirmation of the existence of dark clumps (several of which have been inferred from weak lensing observations) [Sellwood and Kosowsky(2001)].