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Home , Axino, Cold dark matter, Dark matter, Hierarchy problem, Inflation (cosmology), Physical cosmology

Proc. Natl. Acad. Sci. USA Vol. 90, pp. 4827-4834, June 1993 Colloquium Paper

This paper was presented at a colloquium entitled "Physical ," organized by a committee chaired by David N. Schramm, held March 27 and 28, 1992, at the National Academy of , Irvine, CA. Dark : Theoretical perspectives MICHAEL S. TURNER Departments of and of and , , , 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 (, size, or number density), current theoretical prejudice: a flat whose dominant though hope was expressed at this colloquium that new constituent is nonbaryonic , 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 , our knowledge ofQo derives primarily from elementary- , stressing that (i) there are no dynamical estimates that sample small, often atypical envi- dark-matter candidates within the "" of par- ronments (e.g., rich clusters and bright spiral ). 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 , peculiar motion of the , 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 density is accounted dates are a very light (10-6-10-4 eV), a light for by dark matter (i.e., matter that neither emits nor absorbs (20-90 eV), and a heavy (10 GeV-2 TeV). The any ) and that fi0 is at least 0.1-and perhaps as high production of these in the early Universe and the as orderunity. Since primordial 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 , superheavy magnetic mono- left with two possibilities: (i) conclude that Qo lies at its lower poles, and decaying . 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., , matter, and because there are no nonbaryonic dark-matter , 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) ; 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 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- , 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 ofthe Universe) (5). To date these tests have Newtonian dynamics; QCD, Chromodynamics. not been successful because they require standard objects of *A massive neutrino is not considered part of the standard model because neutrino 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 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 , 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- accelerators, and to detect dark- baryonic mass in clusters exists in the form of hot, x-ray matter products (coming from the or the emitting that is "dark" to an (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 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 arises from galaxies inside to assume the mass-to-light ratio derived for the object, or the survey volume and not outside. By using the redshift portion thereof, is "typical" ofthe Universe as a whole. With survey based upon the infrared astronomical satellite 1.2 Jy that as a preface-and a warning-let me proceed. catalogue, two groups have inferred values of C0 that are Mass-to-light ratios derived for the solar neighborhood are close to unity: C0o bl 7 with statistical errors of the order of very small, of the order of unity, and taken as a universal 0.3 (6, 7). Here b (8nGAL/nGAL)/(8p/p) is the so-called bias mass-to-light ratio imply a value of C0 of much less than 1%. factor, which in the simplest way accounts for the fact that Using instead the mass-to-light ratio inferred from the inner bright galaxies may not faithfully trace the mass distribution. luminous regions of spiral and elliptical galaxies, of the order [I should mention that attempts to reconstruct the local of 10 or so, one infers a value for lo of somewhat less than density from the measured peculiar velocity field also 1%. Based upon this evidence, most would agree that lumi- lead to a large value for C0 (7).] nous matter contributes <1% of the critical density (14). To summarize the summary: The flat rotation curves of spiral galaxies give strong (i) Luminous matter (in the form of and associated evidence that most of the mass in spiral galaxies exists in the material) provides at most 1% of the critical density. form of dark halos; assuming that the halo material is (ii) The flat rotation curves of spiral galaxies and virial distributed with spherical (for which there is only masses of clusters indicate that the bulk of the mass density minimal evidence), the density of the halo dark matter in the Universe is dark. decreases as r-2 (15). Many would cite the flat rotation (iii) The dark matter is less condensed than the luminous curves of spiral galaxies as the strongest evidence that most matter (as evidenced by galactic halos). of the material in the Universe is dark. Using the mass-to- (iv) Cl0 is at least 0.1, and the bulk of the data is consistent light ratios derived from the flat rotation curves of spiral with Qo = 0.2 + 0.1 (±0.1 is not a statistical error flag). galaxies, one infers values of Q0o in the range of 3% to 10%. (v) Primordial nucleosynthesis constrains the fraction of Since there is presently no convincing evidence for a rotation critical density contributed by baryons to be between 1% and curve that falls as r-112, indicating convergence of the total 10% (more precisely, 0.01 5 CBh2 S 0.02). mass of the , one should regard these estimates as (vi) There is growing evidence for a gap between CB and lower limits to lo (again, based upon this technique). Qlo. There is some evidence for dark matter in elliptical galaxies A minimalist view is that we have a consistent solution: CB and even dwarfgalaxies, though it is much harder to come by, -loCl 0.1 and h s 0.5. The grander-and more radical- as one must measure velocity dispersions rather than rotation view is that there is a gap between Cl and ClO, that C0 = 1, curves (16, 17). and that we live in a Universe dominated by nonbaryonic The oldest evidence for dark matter, dating back to the dark matter. From a theoretical perspective this is the most work ofZwicky (18), involves clusters; simply put, there isn't attractive scenario-and it may even be true! nearly enough mass associated with the light to hold clusters Three points before we go on; as many have emphasized, together. The masses of clusters are derived using the virial it may well be that there are several kinds ofdark matter (see, theorem and involve certain assumptions: the distribution of e.g., ref. 20). Unless h t 1, primordial nucleosynthesis galactic orbits must be specified and the clusters must be already indicates evidence for dark baryons; moreover, bary- assumed to be "well relaxed." The values for Qio deduced ons could in principle account for all the dark matter in from cluster mass-to-light ratios range from 10% to 30%, galactic halos and possibly even clusters (provided h S 0.5). though we should be mindful of the underlying assumptions Dark baryons could exist in the form of black holes, (current observations seem to indicate that clusters are not stars, or very low mass stars. Three large-scale efforts are well under way to search for dark matter in the form of tIn the BT system, the critical mass-to-light ratio is 1200h, in solar low-mass stars in the halo of our galaxy by using their units. microlensing of stars in the lesser Magellanic cloud (21-23). Downloaded by guest on September 24, 2021 Colloquium Paper: Tumer Proc. Natl. Acad. Sci. USA 90 (1993) 4829

While black holes may appear to the ideal dark-matter below about 300 GeV (down to length scales of the order of candidate, they are not: Black holes formed in the contem- 10-16 cm). They call it the standard model (see, e.g., refs. 33 porary Universe ultimately trace their origins to baryons and and 34); mathematically, it is a non-Abelian thus can contribute no more than about 10% of the critical based upon the group SU(3)c 0g SU(2)L ( U(l)y. The SU(3)c density. While it is possible that mini black holes, holes much part, known as , describes the less massive than a solar mass, were produced in the early strong interactions (the interactions that bind in Universe from the primeval and could today provide ).§ The SU(2)L 0) U(l)y part describes the elec- the critical density, a plausible mechanism for producing the troweak interactions. An important part of the standard right number without other deleterious consequences (e.g., model is the notion that the electromagnetic and weak evaporations today producing too many -y-rays) is interactions are not separate phenomena, but rather different lacking (24-26). aspects of the unified electroweak force. If flo = 1, then the question arises as to where the bulk of The fundamental particles ofthe standard models are three the matter is, because most dynamical measurements indi- families of quarks and (u, d, c, t, and b quarks and ve, cate fl0 0.1-0.3. This is the Q1 problem. It could be that e-, vJL, ,u-, v, and r- leptons) and 12 gauge (eight galactic halos are very large and that clusters sit at the center , W+, W-, ZO, and the ) that mediate the of gigantic distributions of dark matter, that much of the fundamental interactions. All the gauge bosons have been material exists in low-luminosity galaxies (so-called biasing), seen, the top remains to be discovered, and there is or even that it exists in a form of smoothly distributed energy only indirect-but very strong indirect-evidence for the density (e.g., relativistic particles or a cosmological con- existence of the r neutrino. All the particles participate in the stant). In that regard one of the very nice features of neutrino electroweak interactions; only quarks carry color and par- dark matter is that neutrinos, owing to their large , ticipate in the strong interactions. would likely remain smooth on scales out to several mega- While the eight gluons and the photon are massless, the W+ . In any case we know that the dark matter is less and ZO bosons are not; this reflects the least well understood condensed than luminous matter, indicating that it does not aspect of the standard: symmetry breaking. The full symme- have the ability to dissipate energy. This means that it could try of the electroweak interactions is hidden; the simplest be in the form of particles that interact very weakly or could explanation is the and involves a new class be tied up in large objects made of baryons (e.g., dead stars of fundamental (scalar) particles: Higgs bosons, which have or dwarfs). not yet been seen. Hidden symmetry is analogous to the magnetization of a ferromagnet: at low , due to The Evidence for a Flat Universe! spin interactions the state ofthe ferromagnet with lowest free energy is characterized by aligned spins and a net magneti- Before pursuing the hypothesis of a flat Universe dominated zation and thus does not exhibit rotational invariance. The by nonbaryonic dark matter, let me quickly summarize the ground state ofthe Higgs field at low temperatures, due to its evidence in support of it. self-interactions, breaks the symmetry of the electroweak (i) There is evidence for a gap between fIB and flO. interactions and in so doing makes the W+ and ZO bosons (ii) A dynamical explanation for our own peculiar velocity massive (and accounts for the masses of the quarks and seems to indicate that flo is close to unity. leptons as well). The aspects of the standard model involving (iii) Some kinematic measurements of Q10 based upon the gauge particles and quarks and leptons have been tested galaxy counts indicate that 0l0 is close to unity (27, 28). to very high precision (in many cases to better than 1%); there (iv) Structure formation in a low-flO Universe is more is no direct evidence for the Higgs mechanism, and it is difficult and requires larger amplitude density perturbations possible that something else accounts for the hidden sym- and may not be consistent with the observed of the metry. One of the primary motivations for building the CBR (see, e.g., refs. 29 and 30). Superconducting Supercollider is the elucidation of symme- (v) One of the most attractive scenarios of the early try breaking (e.g., by the production of Higgs bosons). Universe, , unambiguously predicts a flat Universe The standard model is a neat little package; in accounting (31). for all "known particle physics," it also explains the absence (vi) According to the Dicke-Peebles timing argument (32), ofother phenomena. For example, why are neutrinos so light if the Universe is not flat, then we must conclude that we live (or perhaps massless)? The SU(2)L symmetry forbids a mass at a special when the terms and matter density for the neutrinos (in the absence of righthanded neutrinos). terms are comparable. Why is the stable (or at least very long-lived)? Again, Needless to say the evidence is not overwhelming; it does, in the standard model it is not possible to have however, make a case for taking the hypothesis of a flat without violating other of the standard model.1 Universe dominated by nonbaryonic dark matter seriously. Similar considerations forbid interactions that violate number. Nonbaryonic Dark Matter New Physics Beyond the Standard Model. The tapestry of the standard model is not without loose threads. Like the If we adopt Do = 1, then the gap between fl0 and QlB is standard cosmology it has shortcomings that point to some- significant and necessitates that a new form of matter be the thing grander; they include dominant constituent of the Universe. The point of this (i) Quantization of charge: quarks and leptons are separate section is to emphasize that particle too were families ofparticles, yet the charges of the quarks are to high pushed to nonbaryonic dark matter for reasons solely based upon particle physics: as a consequence of addressing very §The interactions between hadrons (e.g., between and fundamental problems in particle physics, the existence of ), which used to be referred to as the strong interactions, are new particles was predicted, particles as it turned out whose now believed to be analogous to van der Waals forces, here residual relic cosmic abundance was close to the critical density. This forces between color neutral objects and hence not fundamental could just be a coincidence, or it could be an important hint (see, e.g., ref. 35). $This statement is true at the classical level; subtle quantum effects that we are on the right track. associated with and the like lead to baryon-number The Standard Model of Particle Physics. Over the past two violation. At temperatures ;200 GeV, these processes are probably decades, particle physicists have constructed a fundamental very important and may play a role in explaining the origin of the theory that accounts for all known phenomena at of the Universe (see, e.g., ref. 36). Downloaded by guest on September 24, 2021 4830 Colloquium Paper: Tumer Proc. Natl. Acad. Sci. USA 90 (1993)

precision an integer multiple of one-third the charge of an In almost all models, the lightest is stable and is . a linear combination of the and , known as (ii) A related issue: why are there two kinds of matter the neutralino. The neutralino is a prime dark-matter candi- particles (quarks and leptons) and three families of quarks date. and leptons? Are quarks and leptons fundamental, or are they (iv) (ref. 43): this is a very attractive idea for made of "smaller" entities? replacing the Higgs mechanism with physics that is analogous (iii) Patchwork unification: in the standard model the to that underlying the Bardeen-Cooper-Schreiffer theory of fundamental forces are "patched" together, rather than truly . A stronger version of Quantum Chromo- unified. dynamics (QCD)-technicolor-leads to the formation of (iv) Parameters: the standard model has more than 20 bound states oftechniquarks, and these bound states play the "input parameters" (sin2Ow, quark and lepton masses, mix- role of the Higgs. Technicolor addresses the hierarchy prob- ing angles, etc.) that must be specified. lem, as the mass of the Higgs is set by the energy scale at (v) Disparity of scales: the scale of the which technicolor becomes "strong" (just as the mass of the GF112 300 GeV is much, much less than that of , hadrons is set by the scale at which color becomes strong) and G-1/2 - 1019 GeV (the ""). eliminates the need for scalar particles. However, it is an (vi) A related issue: how is the Higgs to remain light enough attractive idea that has been very difficult to implement: there to break the at a scale of 300 GeV in is currently no viable model of technicolor. Whether or not the face of quantum corrections that should drive its mass to it predicts the existence of dark-matter candidates remains to the highest energy scale in the theory (1019 GeV)? be seen. (vii) The strong-CP problem: within the standard model, (v) Grand unification (see, e.g., ref. 44): the basic goal of quantum effects (instantons again) lead to CP violation in the grand unified (GUTs) is to truly unify the strong, strong interactions and should lead to an electric-dipole weak, and electromagnetic interactions within a single gauge moment for the neutron that is 109 larger than the group with one . The simplest GUT is based current upper limit. of (viii) Unification ofgravity: Where and how does gravity fit upon the gauge group SU(5) and predicts a proton lifetime in? 1030 yr, which, sadly, has been falsified. Other GUTs include most particle physicists to be- SO(10), E6, E8, and on and on. That unification is even These considerations lead possible-given that the coupling strengths of the different lieve that there must be a "grander" theory. Moreover, the remarkable. mathematical tools at hand-non-Abelian gauge theories, interactions are so different at low energies-is , superstrings, to mention three-allow very In non-Abelian gauge theories, coupling strengths vary (or attractive and powerful theoretical speculations that address "run") with energy (logarithmically); the strengths of the all of these issues. These speculations lead to the prediction three known interactions seem to become equal at an energy of new particles, some of which are stable (due to new scale of about 1016 GeV or so, which sets the scale of grand conservation laws) or are at least long-lived (due to their unification. Il Among other things, GUTs predict proton de- small masses and/or very weak interactions). Further-and cay, neutrino masses, and the existence of superheavy mag- this is the cosmological bonus-some of these new, long- netic monopoles (masses of the order of the unification lived particles have relic abundances that are comparable to scale)-the last two being dark-matter candidates. In many the critical density. This didn't have to be; the relic abun- GUTs, neutrino masses arise via the "see-saw mechanism" dance of a particle species is determined by its mass and (45, 46), and min ml/Al, where ml is the charged lepton interactions. This is either the big hint or the grand misdi- mass, and A is an energy scale associated with unification rection. (not necessarily the unification scale itself-perhaps orders To put things in perspective here is a very brief summary ofmagnitude smaller). This explains why neutrino masses are of the extensions of the standard model and the dark-matter so very small-and in many models suggests that neutrinos candidates they predict. may have masses in "the range" (anywhere (i) Peccei-Quinn (PQ) symmetry (37-40): this is a very from microelectronvolts to tens of ). minimal extension of the standard model designed to solve (vi) Superstrings (47, 48): superstring theories unify all the the strong CP problem. It is considered by many to be the forces (including gravity) in a finite quantum theory (WOW!) best solution and automatically arises in many supersymme- and are most naturally formulated in 10 dimensions (suggest- try and superstring models. Another consequence of PQ ing the existence of6 extra spatial dimensions that today must symmetry is the existence of a very long-lived, light (pseu- be compactified). The fundamental objects of the theory are doscalar) particle-the axion-which is a prime dark-matter one-dimensional string-like entities whose size is ofthe order candidate. of 10-33 cm. The expectations for the superstring are high: (ii) models (41): these are modest extensions of ultimately, explanations for everything-quark/lepton the standard model designed to accommodate neutrino mass masses, coupling constants, the strong CP problem, the and thereby allow the three ordinary neutrino species to be number of families, spartner masses, and the electroweak dark-matter candidates. scale. The path has been more difficult than expected, and (iii) Supersymmetry (see, e.g., ref. 42): low-energy super- there have been few definite predictions (that are not wrong). symmetry is perhaps the most well-studied extension of the Broadly, provides theoretical support for standard model. Supersymmetry, the symmetry that relates the axion, supersymmetry, grand unification, and neutrino bosons and , dictates that for every there be masses-providing motivation for all the dark-matter candi- a bosonic partner (and vice versa)-thereby doubling the dates mentioned above. particle content of the standard model. First and foremost, Of course, there are other ideas that I have not mentioned supersymmetry addresses the hierarchy problem, "stabiliz- because at present they do not seem viable-for example, ing" the mass of the Higgs and putting scalar particles , which were postulated as the constituents of quarks on a firm footing. It also paves the way for the unification of gravity (when supersymmetry is gauged, it leads to general "About a decade ago, the convergence of the coupling constants relativity). Supersymmetry must be a broken symmetry since occurred in ordinary GUTs at an energy scale of about 1014 GeV; the known particles do not have equal-mass partners; the better measurements of sin2OW indicate that such a convergence superpartner masses are generically expected to be of the does not occur in nonsupersymmetric GUTs, but does in super- order of 10-1000 GeV (ofthe order of the ). symmetric GUTs at an energy scale of about 1016 GeV. Downloaded by guest on September 24, 2021 Colloquium Paper: Turner Proc. Natl. Acad. Sci. USA 90 (1993) 4831 and leptons, and higher-dimensional analogs of superstrings, I think not, but to convince the reader let me mention two known as membranes. such ideas: fIB - 1 and modified Newtonian dynamics. Two Birds with One Stone. Particle dark matter is attractive Primordial nucleosynthesis provides the best determina- because new particles that owe their existence to attempts to tion of the amount of baryonic matter in the Universe, solve very fundamental puzzles in particle physics have a pinning down the number density of baryons to within a relic abundance of the order of the critical density! Histori- factor of 2. To be sure, the arguments involve assumptions cally, such coincidences have been a sign that one is on the about the Universe in the distant past. Over the , many right track.** have suggested alternative scenarios of primordial nucleo- While there are now literally dozens ofparticle dark-matter synthesis that would allow one to evade the nucleosynthesis candidates, there are but a handful of particles whose pre- bound and have fQB 1 (62). The most recent attempt dicted existence arises due to well-motivated attempts to involved the role of large inhomogeneities that might have solve important problems in particle physics and whose relic been produced in the quark/ transition if it were abundance is in the right ballpark. They are the following: strongly first order. It was hoped that such inhomogeneities (i) The neutralino (52-54). In most supersymmetry models, would allow QB - 1. This possibility is now "double forbid- the neutralino is the lightest supersymmetric partner and is den." As discussed at this colloquium, inhomogeneous nu- stable (due to a new symmetry called R parity). Its interac- cleosynthesis allows very little, if any, loosening of the tions with ordinary matter are roughly the strength of the standard bound (see, e.g., refs. 1-4); moreover, numerical weak interactions, and this fact ultimately explains why its simulations of the quark/hadron transition suggest that such relic abundance is of the order of the critical density. At inhomogeneities would not have arisen in the first place, as that the transition is at best a weakly first-order present, supersymmetric models have many parameters and perhaps not a phase transition at all (more like recom- must be dialed in, and the mass of the neutralino is only bination). known to be somewhere between 10 GeV and 2 TeV. Theorists are rarely criticized for their conservatism! (ii) The axion (55-57). PQ symmetry seems to be the best Moreover, it seems that every theorist worth his salt has tried solution to the nagging strong-CP problem. The mass of the to find a theory of gravity to supplant Einstein's. So one axion depends upon a single parameter: the energy scale of might have expected that theorists would have embraced PQ symmetry breaking,fpQ, and ma - m2X/fpQ - 10-5 eV (1012 Milgrom's modified Newtonian dynamics (MOND) (63, 64). GeV/fpQ). The strength of the axion's couplings to ordinary The basic idea of MOND is that the form ofNewton's second matter is proportional to its mass. When the axion was first law is modified for accelerations less than about cHo - 10-7 invented, only one scale of symmetry breaking was known: cm sec-2, F - ma2/cHo, thereby eliminating the need for the weak scale, and there seemed to be a unique prediction dark matter to explain flat rotation curves. While theorists for its mass, around 200 keV. This idea was quickly falsified. are more than ready to consider modifications to Einstein's It is now realized that there are likely to be many energy theory, especially in light of superstring theory, to most scales in , the GUT scale, the scale, the theorists MOND looks like a nonstarter. The reason is intermediate scale, and so on. The symmetry-breaking scale simple: it is purely a Newtonian theory, and attempts to has been constrained, largely by astrophysical and cosmo- formulate it in terms of a relativistic field theory have been logical arguments, to lie in the interval 1010 GeV !fpQ 5 1013 unsuccessful. Without such a formulation, one cannot con- GeV, corresponding to an axion mass in the range 10-6_10-3 struct a cosmological model or evaluate its predictions for the eV (58, 59). This also happens to be the range where the relic many tests we have of relativistic theories of gravity- abundance of is of the order of the critical density. bending of starlight, precession of the perihelion of Mercury, (iii) The light neutrino. The neutrino exists; it comes in , radar time delay, and the myriad of three varieties; and we know its relic abundance to three tests offered by the binary . If that were not bad significant figures, 113 cm-3 per species. Further, essentially enough, it has been argued that MOND can be falsified on the all extensions of the standard model predict that neutrinos basis of rotation curves measured for galaxies of very differ- have mass, and the see-saw mechanism implies masses in the ent sizes (65, 66). general range of electronvolts, give or take a factor of 103 or In sum, theorists have looked hard for other explanations; so. I believe that it is fair to say that the particle dark-matter (iv) Dark horses. There are also a few well-motivated long explanation is the most attractive. Whether or not it proves shots. They include the superheavy : it is to be correct is another matter. a generic prediction of GUTs; the only problem is its abun- dance; without inflation far too many monopoles are pro- Dark-Matter Relics: Origins duced; and with inflation essentially no monopoles are pro- duced (see, e.g., ref. 60). There is the supersymmetric partner Since an important motivation for particle dark matter is the of the axion, the , which arises in theories with both PQ fact that the relic abundance of these handful of promising symmetry and supersymmetry (61). Its mass is expected to be candidates is comparable to the critical density, it is worth in the kiloelectrovolt range, and its abundance is significantly reviewing how a cosmological relic arises. There are several less than neutrinos as it decouples much earlier. qualitatively different mechanisms for particle dark-matter Why Not Baryons or Modified Gravity? The particle dark- production in the early Universe. matter hypothesis is a radical solution; are there other Thermal Relics: Hot, Warm, and Cold. Much, but not all, alternatives that are less radical or perhaps more attractive? of the history of the Universe is characterized by thermal equilibrium. So long as equilibrium pertains, the abundance of a massive particle relative to photonstt is of the order **For a while, some believed that one could get three birds with one of for T >> and of the order of stone: cosmions, dark-matter particles of mass 4-10 GeV with unity temperatures m/3 cross sections of the order of 10-35 cm2, were proposed to solve both the solar-neutrino and the dark-matter problems. ttThe number of particles per comoving volume, R3n, is actually This possibility is all but ruled out on both theoretical grounds- proportional to the ratio of the particle number density to the the corresponding annihilation cross section leads to a cosmion density, nls, where s X g*T3 and g* counts the effective abundance that is too small in both the sun and the -and number of ultrarelativistic degrees of freedom. So long as g* is experimental grounds-cosmions should have been detected in constant, s and n, are related by a constant numerical factor, today dark-matter searches (49-51). about 7.04. Downloaded by guest on September 24, 2021 4832 Colloquium Paper: Tumer Proc. Natl. Acad. Sci. USA 90 (1993) (m/T)3/2 exp(-m/T) for T << m/3. For reference, the fraction of critical density contributed by a relic species is fkxh2 - lo) MG [31

Qh~(m ) n)1 where qx is the particle- asymmetry relative to photons. A stable neutrino species with mass of the order of 100 GeV and asymmetry of the order of the baryon asym- If equilibrium were the entire story, relic abundances would metry could provide closure density. [Neither the precision be far too small to be of any interest. measurements of the width of the ZO boson nor nucleosyn- Consider a stable, massive particle species; its abundance thesis precludes such a fourth neutrino species; dark-matter is necessarily regulated by and pair creations. In searches employing detectors do unless the mass the expanding Universe, the is decreasing, TIT exceeds a teraelectronvolt or so (79-82)]. - -H; equilibrium can be maintained only if annihilations Nonthermal Relics. The magnetic monopole and axion are and pair creations occur rapidly on the expansion time scale, examples of particles whose relic abundance involves coher- H-1. Because of the temperature dependence of equilibrium ent, nonthermal processes. Monopoles are produced as (point- number densities and of cross sections, annihilation and pair like topological) defects in the GUT symmetry-breaking phase creation reactions eventually become ineffective ("freeze transition (see, e.g., ref. 60). On the basis of con- out"), and the abundance of a particle species relative to siderations, one expects of the order of one monopole per photons approaches a constant value ("freezes in") (67-70). horizon volume (at the time of the phase transition), which If freeze out occurs when the species is relativistic, then leads to a relic abundance of order n/ny - (T/mpl)3. For the the species' relic abundance is comparable to that ofphotons. GUT phase transition, T - 1015 GeV or so, which results in a Such a species is referred to as a hot relic; a light (mass s gross overabundance of monopoles (very crudely, "Ql - megaelectronvolts) neutrino species is a hot relic. 1012"). This is the monopole problem. Inflation can solve the On the other hand, if freeze out occurs when the species is monopole problem provided that the GUT phase transition nonrelativistic, then its relic abundance is significantly less occurs before inflation, so that monopoles are diluted by the than that of photons and depends inversely upon its annihi- massive entropy production. This being said, it appears that lation cross section (in thermal equilibrium, the annihilation monopoles are a terrible dark-matter candidate; however, rate and pair creation rate are related by detailed balance). scenarios have been proposed where their relic abundance can The relic abundance is be close to critical (see, e.g., ref. 60). Axions arise not only as thermal relics but also due to two n ln(0.01mmpj(crV)ann) 10-3 nonthermal processes, the misalignment process and the decay of axionic strings (58, 59). For the interesting axion kny MMPJ(O'V)ann TOMP1(av)ann masses, 10-6-10-4 eV, their thermal relic abundance cannot where the second relation follows from the fact that PCRIT - come close to closure density. Since there is some disagree- 104To. This formula is quite remarkable: neglecting the ment as to the importance ofthe axionic string decay process logarithmic factor and the overall numerical constant, it (83-86) and it is impotent in an inflationary Universe, I will implies that the fraction of critical density contributed by a focus on the misalignment process (55-57). cold relic only depends upon its annihilation cross section It is the 0 parameter of QCD that leads to the strong-CP and, further, that Ql - 1 obtains for (av)ann - 10-3/Tompi - problem; 0 is an angular parameter that controls the strength 10-37 cm2! This is very roughly a weak-interaction cross of the offending effects. In the PQ solution, 0 section (=GeV2GF2) and indicates that a stable particle with becomes a dynamical variable whose value is anchored at the weak interactions will necessarily have a relic abundance CP-conserving value of zero by the instanton effects them- comparable to the critical density. A stable neutrino of mass selves. However, at temperatures much greater than 1 GeV, of a few gigaelectronvolts would fit the bill were it not ruled these effects are impotent, and the value of 0 is left unde- out by experiment (71-75). The neutralino fits the bill nicely, termined by dynamical considerations. Thus, one expects the as its interactions with ordinary matter are roughly weak. value of 0 to be randomly distributed in different causally The final case is . If a species decouples independent regions of the Universe. When the QCD instan- while it is still relativistic, but very early on (T >> 1 GeV), ton effects do become important, 0 will in general be then after it decouples its abundance relative to photons will "misaligned" (i.e., not at 0 = 0) and will evolve toward 0 = be diminished as various species disappear and transfer their 0; as it does, 0 overshoots and is left oscillating. These entropy to the photons (and other species). In this case, its cosmic harmonic oscillations correspond to a condensate of abundance is less than that of photons, but not exponentially very nonrelativistic axions, whose relic density is roughly less, and so closure density obtains for masses in the kiloelec- tronvolt range; plausible warm dark-matter candidates include Qlh2~= ( eV)m -1.2 [4] the axino (61) and a light (76). (This dilution by 10-' eVX "entropy transfer" is precisely what makes the relic neutrino temperature and abundance less than that of photons.) The energy associated with the misalignment of 0 is con- Skew Relics. Implicit in the previous discussion is the verted into an enormous number of axions, about 109 cm-3 assumption that the particle and its antiparticle were equally for ma = 10-5 eV. abundant. If there is an asymmetry between particle and Signicant Other Relics. While our first interest is in eluci- antiparticle and net particle number is conserved, then the dating the nature of the ubiquitous dark matter, it is possible relic abundance can become no smaller than the net particle that there are a number ofparticle relics in our midst. Needless number per photon (see, e.g., ref. 77). Provided that annihi- to say, a particle relic that contributes significantly less than lations can reduce the particle's abundance to this level, the closure could still be interesting-both from the point of view relic abundance is determined by the particle-antiparticle of cosmology and of particle physics; moreover, it could be asymmetry. detectable. The CBR provides such an example: l.y - 10-4. Baryons are an example of a skew relic; if not for the Until it was ruled out by a telescope search for its decays, an asymmetry between baryons and antibaryons, the relic abun- electronvolt-mass axion provided another possibility (87, 88). dance of each would be about 10-18 that of photons (78). The If Nature is supersymmetric and the lightest supersymmetry mass density contributed by a skew relic is particle is stable, it is difficult to avoid a supersymmetric relic Downloaded by guest on September 24, 2021 Cofloquium Paper: Tumer Proc. Natl. Acad. Sci. USA 90 (1993) 4833 that contributes less than about 10-3 of closure density. First, there are the direct schemes, where the halo dark- Magnetic monopoles provide yet another example. If the matter particles in our local neighborhood (density 5 x 10-25 earliest history ofthe Universe is as interesting as many think, g.cm-3) are sought out. For axions, the approach is based there may be many relics whose abundance is far from critical upon a very clever idea of Sikivie (110) that takes advantage but are still potentially detectable. of the axion's coupling to two photons. A cavity Truly Exotic Relics. Other more complicated explanations is immersed in a very strong magnetic field, which causes for the dark-matter problem involving early Universe relics halo axions to be converted to photons and excites resonant have been suggested. Two suggestions have been made that modes of the cavity; several "proof of principle experi- would reconcile a flat Universe with the observational data ments" have been built and operated, and a new generation that the amount of matter that clusters contributes only 20% of Sikivie detectors with sufficient sensitivity to detect halo or so of critical density: a "relic cosmological constant" and axions are being built (111). Neutralino detectors exploit the dark matter that decays at a modest redshift into relativistic neutralino's roughly weak interactions with ordinary matter: debris, which necessarily remains unclustered (89-92). In when a multi-gigaelectronvolt mass neutralino scatters off a either case, dynamical measurements of fl0 would not reveal nucleus, it deposits an energy oforder a kiloelectronvolt. The the unclustered - energy or relativ- annihilation cross section and elastic cross section are related istic particles-and would yield values of the order of 20%. by "crossing," and thus the scattering cross section too On the other hand, kinematic measurements could reveal the should be of the order of 10-7 cm2; this implies an event rate presence of the unclustered energy density (93). In either of the order of 1 per day per kg. A new generation of case, a new cosmic coincidence comes into play: a cosmo- low-background, low-threshold cryogenic detectors are be- logical constant that becomes dynamically important in the ing developed to search for in our halo. While the current epoch or a particle whose lifetime is comparable to the age of the Universe. magnetic monopole must be considered a long-shot dark- A relic cosmological constant provokes further discussion. matter candidate, a football field-sized detector called Historically, cosmologists have turned to the cosmological MACRO is just coming on line and will achieve a sensitivity constant when faced with a crisis. In the context of of about 10-16 cm-2 sr-1 sec-l (113). quantum- are field theory, it is actually the absence of an enormous (A - Next, there indirect searches, which involve seeking 10122 G-1) cosmological constant associated with the zero- out the decay or annihilation products of dark-matter parti- point energy of quantum fluctuations of the fundamental cles. For example, dark-matter annihilations in the halo of fields that is a mystery. To confuse the situation further, our galaxy can produce high-energy that can be several authors have argued that a Universe with a cosmo- detected (114-116). The most promising idea involves anni- logical constant, , and baryons is currently hilations of dark-matter particles that accumulate in the sun the best-fit Universe, in terms of the age of the Universe, and the (117-119); the annihilation products include dynamical measurements of flo, and the formation of struc- high-energy neutrinos that can be detected in large, under- ture (94, 95). ground earth-based detectors, such as MACRO (113). A Other puzzles have motivated suggestions for "specialized sizable portion of the neutralino parameter can be relics." Sciama and others (96-100) have argued for an explored by searching for high-energy neutrinos from the sun unstable neutrino species whose radiative decays would lead and the earth (112). to efficient of the Universe. Recently, "cock- Finally, there are numerous laboratory and astrophysical tails" of two particle relics-30% neutrinos and 70% cold experiments that bear on the existence of particle dark dark matter-have been advocated to make the cold dark- matter. Searches for the supersymmetric partners of the matter scenario for structure formation better agree with known particles are taking place at every accelerator in the observations (101-105). ; the discovery ofeven one superpartner would not only A New Cosmic Ratio. If the bulk of the mass density is in provide strong evidence for the existence of the neutralino the form of nonbaryonic dark matter, then cosmologists- but would also help to narrow the parameter space. There are and particle physicists-have a new dimensionless number to a host of experiments that bear on the issue of neutrino explain: the ratio of ordinary matter to . Why is masses: experiments designed to measure the electron- it of the order of unity and not say 10-20 or 1020? The value neutrino mass, /mixing experiments, so- of this ratio has important consequences for the of lar neutrino experiments, and searches for neutrinos from the Universe, and the fact that it is of the order of unity is at type II supernovae. the heart of many cosmological observations (e.g., the halo/ disk conspiracy in rotation curves, the stability of galactic Concluding Remarks disks, and even the formation of stars). Although there is presently no good explanation for why The theorists' prejudice of a flat Universe dominated by this ratio is of the order of unity, it necessarily involves nonbaryonic dark matter is at present just that! However, I fundamental physics. For example, consider a skew relic hope that I have convinced the reader that (i) the dark-matter whose asymmetry is comparable to the baryon asymmetry; question is a most pressing one, which now involves both then the ratio is just that of the exotic particle's mass to the cosmologists and particle physicists; (ii) the theorists' prej- mass of a baryon. For other relics, requiring that this ratio be udice is well motivated by both theoretical and observational of the order of unity implies special relationships between considerations; and (iii) most importantly, the particle dark- fundamental energy scales in physics (106). matter hypothesis can and is being tested. While cosmolog- ical experiments are inherently difficult and we cannot test Detection every dark-matter candidate, I am optimistic. The most promising dark-matter candidates are detectable, and the The nonbaryonic dark-matter hypothesis is a very bold one, dark-matter problem has attracted the attention of many of and fortunately it is testable. While no cosmological exper- the most talented experimentalists from both cosmology and iment or observation is easy, especially the search for a particle physics. While this is no guarantee that we will have particle whose interactions could be as different as those of an answer soon, what more could one ask? And if that isn't an axion and a neutralino, thanks to the creative efforts of enough, there is the payoff: identifying and quantifying the many, there are manifold approaches to the problem of primary substance of the Universe and discovering "new detection (see, e.g., 107-109). physics" in the process! Downloaded by guest on September 24, 2021 4834 Cofloquium Paper: Tumer Proc. Natl. Acad. Sci. USA 90 (1993)

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