Proc. Natl. Acad. Sci. USA Vol. 90, pp. 4827-4834, June 1993 Colloquium Paper This paper was presented at a colloquium entitled "Physical Cosmology," organized by a committee chaired by David N. Schramm, held March 27 and 28, 1992, at the National Academy of Sciences, Irvine, CA. Dark matter: Theoretical perspectives MICHAEL S. TURNER Departments of Physics and of Astronomy and Astrophysics, Enrico Fermi Institute, University of Chicago, Chicago, IL 60637-1433; and Theoretical Astrophysics, Fermi National Accelerator Laboratory, Batavia, IL 60510-0500 ABSTRACT I both review and make the case for the one sort or another (luminosity, size, or number density), current theoretical prejudice: a flat Universe whose dominant though hope was expressed at this colloquium that new constituent is nonbaryonic dark matter, emphasizing thatthis is techniques may change this situation (e.g., K-band Hubble still a prejudice and notyetfact. The theoretical motivation for diagram, K-band number counts, type I or II supernovae, and nonbaryonic dark matter is discussed in the context of current so on). At present, our knowledge ofQo derives primarily from elementary-particle theory, stressing that (i) there are no dynamical estimates that sample small, often atypical envi- dark-matter candidates within the "standard model" of par- ronments (e.g., rich clusters and bright spiral galaxies). There ticle physics, (ii) there are several compelling candidates within is an exception, the recent attempts to infer Qo based upon the attractive extensions of the standard model of particle physics, peculiar motion of the Local Group, which interestingly and (ii) the motivation for these compelling candidates comes enough yield a value for Qo oforder unity and with small error first and foremost from particle physics. The dark-matter estimates (6, 7). Beyond the fact that this measurement problem is now a pressing issue in both cosmology and particle supports theoretical prejudice, it may well come the closest to physics, and the detection of particle dark matter would weighing a large, fair sample of the Universe. provide evidence for "new physics." The compelling candi- What is clear is that most of the mass density is accounted dates are a very light axion (10-6-10-4 eV), a light neutrino for by dark matter (i.e., matter that neither emits nor absorbs (20-90 eV), and a heavy neutralino (10 GeV-2 TeV). The any radiation) and that fi0 is at least 0.1-and perhaps as high production of these particles in the early Universe and the as orderunity. Since primordial nucleosynthesis provides very prospects for their detection are also discussed. I briefly convincing evidence that baryonic matter can contribute no mention more exotic possibilities for the dark matter, including more than 10l%o of critical density (see, e.g., refs. 1-4), we are a nonzero cosmological constant, superheavy magnetic mono- left with two possibilities: (i) conclude that Qo lies at its lower poles, and decaying neutrinos. bound, that QB lies at its upper boundary, and that h S 0.5, in which case nOo QB = 0.1; or (ii) conclude that there is a Overview "gap" between no and QIB and consider the consequences. While the second possibility is the more radical, the evi- One of the simplest yet most fundamental questions we can dence for a gap, though not yet conclusive, continues to ask in cosmology concerns the quantity and composition of mount. If we accept this gap as real and make the leap all the the matter in the Universe: What is mass density, QO, way to a flat Universe, there are important implications: by a expressed as a fraction of the critical density, and what are wide margin, most ofthe Universe is made up ofnonbaryonic the contributions of the various constituents-e.g., baryons, matter, and because there are no nonbaryonic dark-matter photons, and whatever else? [The critical density PCRIT = candidates within the "standard model" of the elementary 3H0/8irG = 1.88h2 x 10-29 g-cm3 = 1.05 x 104 eV-cm3, particles, the dark-matter problem becomes one of pressing where Ho = 100h km sec-1 Mpc-1; 1 eV = 1.602 x 10-19 J; interest in particle physics also. Particle physics rises to the 1 megaparsec (Mpc) = 3.09 x 1022 m.] The answer to this occasion: in several of the most attractive extensions of their question bears upon almost every topic discussed at this standard model there are hypothetical particles whose moti- colloquium: the expansion age and fate of the Universe; the vations are unrelated to cosmology, but whose relic abun- origin of structure in the Universe and cosmic background dance is close to the closure density. The most promising are radiation (CBR) anisotropies; galactic disks, rotation curves, an axion of mass 10-6 eV-10-4 eV, a neutralino of mass 10 and morphology; cluster dynamics; gravitational lensing; and GeV-2 TeV, and a neutrino of mass 90h2 eV.* the distribution of light and mass. The only thing we know Most theorists would agree that a flat Universe dominated with great precision is the contribution of photons, nZ = by nonbaryonic matter is the most attractive hypothesis, so 2.49h-2 X 10-4 (assuming Tyo = 2.73 K), and neutrinos, Ql, attractive that it is sometimes forgotten that it is stilljust that. = 1.70h-2 X 10-4 (assuming all three species are massless); This paradigm has become an almost indispensable crutch for and based on primordial nucleosynthesis, we know the those who study the formation of structure. In fact, I know contribution of baryons to within a factor of two, nBh2 = of no viable model of structure formation based upon a 0.01-0.02 (see, e.g., refs. 1-4). Universe with no = nB Y 0.1.t In principle, the classic kinematic tests-luminosity- redshift, angular size-redshift, number count-redshift, and so Abbreviations: CBR, cosmic background radiation; GUT, grand on-can be used to determine no (provided that we know the unified theory; PQ, Peccei-Quinn; MOND, Milgrom's modified equation of state ofthe Universe) (5). To date these tests have Newtonian dynamics; QCD, Quantum Chromodynamics. not been successful because they require standard objects of *A massive neutrino is not considered part of the standard model because neutrino masses are not accommodated within the standard model of particle physics. The publication costs of this article were defrayed in part by page charge tPeebles's isocurvature baryon model comes close, but as I under- payment. This article must therefore be hereby marked "advertisement" stand it, the model requires that QlB - 0.2 and h - 0.8 (refs. 8 and in accordance with 18 U.S.C. §1734 solely to indicate this fact. 9). 4827 Downloaded by guest on September 24, 2021 4828 Colloquium Paper: Tumer Proc. Natl. Acad. Sci. USA 90 (1993) That being the case, it is important that we take our well relaxed) and the fact that any material that is distributed theoretical beliefs seriously enough to test them! At our spherically symmetrically outside the region where galaxies disposal are a host of laboratory experiments and observa- reside would not contribute to the virial masses derived. And tional tests. They include cosmological measurements of Cl0, of course, the fundamental assumption is that cluster mass- Ho, the age of the Universe, CBR anisotropies, large-scale to-light ratios are typical, though less than 1 in 10 galaxies structure, and so on. In the laboratory there are efforts to resides in a cluster. We should note too that dark is a relative directly detect halo dark-matter particles, to produce new term: it is now known that much, if not the majority, of the particles at high-energy accelerators, and to detect dark- baryonic mass in clusters exists in the form of hot, x-ray matter annihilation products (coming from the sun or the emitting gas that is "dark" to an optical telescope (see, e.g., halo), as well as a multitude of experiments that search for ref. 19). evidence for neutrino masses. The virial masses of small groups and binary galaxies also provide evidence for dark matter, though the problem of Weighing the Universe interlopers is a severe one. The gravitational arcs produced by the lensing effect of clusters also indicate the presence of Neither measuring the mean density of the Universe nor cluster dark matter. Evidencefor dark matter in the Universe summarizing the measurements and putting them in perspec- is nowhere lacking. tive is a simple task (for a review, see refs. 10-13). Simply In my biased and very briefsummary, I have saved the best put, one would like to weigh a representative volume of the for last, a measurement that comes close to weighing a Universe, say lOOh-1 Mpc on a side. This is easier said than representative sample of the Universe of order lOOh-I Mpc done. Because of the inconclusiveness of the kinematic on a side. It involves tying our well-measured velocity with methods, I will focus on the dynamical measurements. respect to the CBR, about 620 km sec-1, to the inhomoge- The neous distribution ofmatter in the nearby Universe. In effect, dynamical measurements probe the mean density in a it is a simple problem in Newtonian physics: requiring our less than ideal way: a dynamical measurement (e.g., the virial velocity be produced by the inhomogeneous distribution of mass of a cluster) is converted into a mass-to-light ratio, galaxies allows us to weigh a very large sample of the which, when multiplied by the mean luminosity density Universe. Two important assumptions are made: that the (which itself has to be determined), yields an estimate of the distribution ofgalaxies traces the mass at some level and that mean mass density.* There is an obvious drawback: one has the bulk of our peculiar velocity arises from galaxies inside to assume the mass-to-light ratio derived for the object, or the survey volume and not outside.