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

This paper was presented at a colloquium entitled "Physical Cosmology," organized by a committee chaired by DavidN. Schramm, held March 27 and 28, 1992, at the National Academy of Sciences, Irvine, CA.

Dark matter: Theoretical perspectivesMICHAEL S. TURNERDepartments of Physics and of Astronomy and Astrophysics, Enrico Fermi Institute, University of Chicago, Chicago, IL 60637-1433; and TheoreticalAstrophysics, Fermi National Accelerator Laboratory, Batavia, IL 60510-0500

ABSTRACT I both review and make the case for thecurrent theoretical prejudice: a flat Universe whose dominantconstituent is nonbaryonic dark matter, emphasizing that this isstill a prejudice and not yetfact. The theoretical motivation fornonbaryonic dark matter is discussed in the context of currentelementary-particle theory, stressing that (i) there are nodark-matter candidates within the "standard model" of par-ticle physics, (ii) there are several compelling candidates withinattractive extensions of the standard model of particle physics,and (ii) the motivation for these compelling candidates comesfirst and foremost from particle physics. The dark-matterproblem is now a pressing issue in both cosmology and particlephysics, and the detection of particle dark matter wouldprovide evidence for "new physics." The compelling candi-dates are a very light axion (10-6-10-4 eV), a light neutrino(20-90 eV), and a heavy neutralino (10 GeV-2 TeV). Theproduction of these particles in the early Universe and theprospects for their detection are also discussed. I brieflymention more exotic possibilities for the dark matter, includinga nonzero cosmological constant, superheavy magnetic mono-poles, and decaying neutrinos.

Overview

One of the simplest yet most fundamental questions we canask in cosmology concerns the quantity and composition ofthe matter in the Universe: What is mass density, QO,expressed as a fraction of the critical density, and what arethe contributions of the various constituents-e.g., baryons,photons, and whatever else? [The critical density PCRIT =3H0/8irG = 1.88h2 x 10-29 g-cm3 = 1.05 x 104 eV-cm3,where Ho = 100h km sec-1 Mpc-1; 1 eV = 1.602 x 10-19 J;1 megaparsec (Mpc) = 3.09 x 1022 m.] The answer to thisquestion bears upon almost every topic discussed at thiscolloquium: the expansion age and fate of the Universe; theorigin of structure in the Universe and cosmic backgroundradiation (CBR) anisotropies; galactic disks, rotation curves,and morphology; cluster dynamics; gravitational lensing; andthe distribution of light and mass. The only thing we knowwith great precision is the contribution of photons, nZ =2.49h-2 X 10-4 (assuming Tyo = 2.73 K), and neutrinos, Ql,= 1.70h-2 X 10-4 (assuming all three species are massless);and based on primordial nucleosynthesis, we know thecontribution of baryons to within a factor of two, nBh2 =0.01-0.02 (see, e.g., refs. 1-4).

In principle, the classic kinematic tests-luminosity-redshift, angular size-redshift, number count-redshift, and soon-can be used to determine no (provided that we know theequation of state of the Universe) (5). To date these tests havenot been successful because they require standard objects of

The publication costs of this article were defrayed in part by page chargepayment. This article must therefore be hereby marked "advertisement"in accordance with 18 U.S.C. §1734 solely to indicate this fact.

one sort or another (luminosity, size, or number density),though hope was expressed at this colloquium that newtechniques may change this situation (e.g., K-band Hubblediagram, K-band number counts, type I or II supernovae, andso on). At present, our knowledge ofQo derives primarily fromdynamical estimates that sample small, often atypical envi-ronments (e.g., rich clusters and bright spiral galaxies). Thereis an exception, the recent attempts to infer Qo based upon thepeculiar motion of the Local Group, which interestinglyenough yield a value for Qo of order unity and with small errorestimates (6, 7). Beyond the fact that this measurementsupports theoretical prejudice, it may well come the closest toweighing a large, fair sample of the Universe.What is clear is that most of the mass density is accounted

for by dark matter (i.e., matter that neither emits nor absorbsany radiation) and that fi0 is at least 0.1-and perhaps as highas order unity. Since primordial nucleosynthesis provides veryconvincing evidence that baryonic matter can contribute nomore than 10l%o of critical density (see, e.g., refs. 1-4), we areleft with two possibilities: (i) conclude that Qo lies at its lowerbound, that QB lies at its upper boundary, and that h S 0.5, inwhich case nOo QB = 0.1; or (ii) conclude that there is a"gap" between no and QIB and consider the consequences.While the second possibility is the more radical, the evi-

dence for a gap, though not yet conclusive, continues tomount. If we accept this gap as real and make the leap all theway to a flat Universe, there are important implications: by awide margin, most of the Universe is made up of nonbaryonicmatter, and because there are no nonbaryonic dark-mattercandidates within the "standard model" of the elementaryparticles, the dark-matter problem becomes one of pressinginterest in particle physics also. Particle physics rises to theoccasion: in several of the most attractive extensions of theirstandard model there are hypothetical particles whose moti-vations are unrelated to cosmology, but whose relic abun-dance is close to the closure density. The most promising arean axion of mass 10-6 eV-10-4 eV, a neutralino of mass 10GeV-2 TeV, and a neutrino of mass 90h2 eV.*Most theorists would agree that a flat Universe dominated

by nonbaryonic matter is the most attractive hypothesis, soattractive that it is sometimes forgotten that it is stilljust that.This paradigm has become an almost indispensable crutch forthose who study the formation of structure. In fact, I knowof no viable model of structure formation based upon aUniverse with no = nB Y 0.1.t

Abbreviations: CBR, cosmic background radiation; GUT, grandunified theory; PQ, Peccei-Quinn; MOND, Milgrom's modifiedNewtonian dynamics; QCD, Quantum Chromodynamics.*A massive neutrino is not considered part of the standard modelbecause neutrino masses are not accommodated within the standardmodel of particle physics.

tPeebles's isocurvature baryon model comes close, but as I under-stand it, the model requires that QlB - 0.2 and h - 0.8 (refs. 8 and9).

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That being the case, it is important that we take ourtheoretical beliefs seriously enough to test them! At ourdisposal are a host of laboratory experiments and observa-tional tests. They include cosmological measurements of Cl0,Ho, the age of the Universe, CBR anisotropies, large-scalestructure, and so on. In the laboratory there are efforts todirectly detect halo dark-matter particles, to produce newparticles at high-energy accelerators, and to detect dark-matter annihilation products (coming from the sun or thehalo), as well as a multitude of experiments that search forevidence for neutrino masses.

Weighing the Universe

Neither measuring the mean density of the Universe norsummarizing the measurements and putting them in perspec-tive is a simple task (for a review, see refs. 10-13). Simplyput, one would like to weigh a representative volume of theUniverse, say lOOh-1 Mpc on a side. This is easier said thandone. Because of the inconclusiveness of the kinematicmethods, I will focus on the dynamical measurements.The dynamical measurements probe the mean density in a

less than ideal way: a dynamical measurement (e.g., the virialmass of a cluster) is converted into a mass-to-light ratio,which, when multiplied by the mean luminosity density(which itself has to be determined), yields an estimate of themean mass density.* There is an obvious drawback: one hasto assume the mass-to-light ratio derived for the object, orportion thereof, is "typical" of the Universe as a whole. Withthat as a preface-and a warning-let me proceed.

Mass-to-light ratios derived for the solar neighborhood arevery small, of the order of unity, and taken as a universalmass-to-light ratio imply a value of C0 of much less than 1%.Using instead the mass-to-light ratio inferred from the innerluminous regions of spiral and elliptical galaxies, of the orderof 10 or so, one infers a value for lo of somewhat less than1%. Based upon this evidence, most would agree that lumi-nous matter contributes <1% of the critical density (14).The flat rotation curves of spiral galaxies give strong

evidence that most of the mass in spiral galaxies exists in theform of dark halos; assuming that the halo material isdistributed with spherical symmetry (for which there is onlyminimal evidence), the density of the halo dark matterdecreases as r-2 (15). Many would cite the flat rotationcurves of spiral galaxies as the strongest evidence that mostof the material in the Universe is dark. Using the mass-to-light ratios derived from the flat rotation curves of spiralgalaxies, one infers values of Q0o in the range of 3% to 10%.Since there is presently no convincing evidence for a rotationcurve that falls as r-112, indicating convergence of the totalmass of the galaxy, one should regard these estimates aslower limits to lo (again, based upon this technique).There is some evidence for dark matter in elliptical galaxies

and even dwarf galaxies, though it is much harder to come by,as one must measure velocity dispersions rather than rotationcurves (16, 17).The oldest evidence for dark matter, dating back to the

work ofZwicky (18), involves clusters; simply put, there isn'tnearly enough mass associated with the light to hold clusterstogether. The masses of clusters are derived using the virialtheorem and involve certain assumptions: the distribution ofgalactic orbits must be specified and the clusters must beassumed to be "well relaxed." The values for Qio deducedfrom cluster mass-to-light ratios range from 10% to 30%,though we should be mindful of the underlying assumptions(current observations seem to indicate that clusters are not

tIn the BT system, the critical mass-to-light ratio is 1200h, in solarunits.

well relaxed) and the fact that any material that is distributedspherically symmetrically outside the region where galaxiesreside would not contribute to the virial masses derived. Andof course, the fundamental assumption is that cluster mass-to-light ratios are typical, though less than 1 in 10 galaxiesresides in a cluster. We should note too that dark is a relativeterm: it is now known that much, if not the majority, of thebaryonic mass in clusters exists in the form of hot, x-rayemitting gas that is "dark" to an optical telescope (see, e.g.,ref. 19).The virial masses of small groups and binary galaxies also

provide evidence for dark matter, though the problem ofinterlopers is a severe one. The gravitational arcs producedby the lensing effect of clusters also indicate the presence ofcluster dark matter. Evidencefor dark matter in the Universeis nowhere lacking.

In my biased and very briefsummary, I have saved the bestfor last, a measurement that comes close to weighing arepresentative sample of the Universe of order lOOh-I Mpcon a side. It involves tying our well-measured velocity withrespect to the CBR, about 620 km sec-1, to the inhomoge-neous distribution ofmatter in the nearby Universe. In effect,it is a simple problem in Newtonian physics: requiring ourvelocity be produced by the inhomogeneous distribution ofgalaxies allows us to weigh a very large sample of theUniverse. Two important assumptions are made: that thedistribution of galaxies traces the mass at some level and thatthe bulk of our peculiar velocity arises from galaxies insidethe survey volume and not outside. By using the redshiftsurvey based upon the infrared astronomical satellite 1.2 Jycatalogue, two groups have inferred values of C0 that areclose to unity: C0o bl 7 with statistical errors of the order of0.3 (6, 7). Here b (8nGAL/nGAL)/(8p/p) is the so-called biasfactor, which in the simplest way accounts for the fact thatbright galaxies may not faithfully trace the mass distribution.[I should mention that attempts to reconstruct the localdensity field from the measured peculiar velocity field alsolead to a large value for C0 (7).]To summarize the summary:(i) Luminous matter (in the form of stars and associated

material) provides at most 1% of the critical density.(ii) The flat rotation curves of spiral galaxies and virial

masses of clusters indicate that the bulk of the mass densityin the Universe is dark.

(iii) The dark matter is less condensed than the luminousmatter (as evidenced by galactic halos).

(iv) Cl0 is at least 0.1, and the bulk of the data is consistentwith Qo = 0.2 + 0.1 (±0.1 is not a statistical error flag).

(v) Primordial nucleosynthesis constrains the fraction ofcritical density contributed by baryons to be between 1% and10% (more precisely, 0.01 5 CBh2 S 0.02).

(vi) There is growing evidence for a gap between CB andQlo.A minimalist view is that we have a consistent solution: CB

-loCl 0.1 and h s 0.5. The grander-and more radical-view is that there is a gap between Cl and ClO, that C0 = 1,and that we live in a Universe dominated by nonbaryonicdark matter. From a theoretical perspective this is the mostattractive scenario-and it may even be true!Three points before we go on; as many have emphasized,

it may well be that there are several kinds of dark matter (see,e.g., ref. 20). Unless h t 1, primordial nucleosynthesisalready indicates evidence for dark baryons; moreover, bary-ons could in principle account for all the dark matter ingalactic halos and possibly even clusters (provided h S 0.5).Dark baryons could exist in the form of black holes, neutronstars, or very low mass stars. Three large-scale efforts arewell under way to search for dark matter in the form oflow-mass stars in the halo of our galaxy by using theirmicrolensing of stars in the lesser Magellanic cloud (21-23).

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While black holes may appear to the ideal dark-mattercandidate, they are not: Black holes formed in the contem-porary Universe ultimately trace their origins to baryons andthus can contribute no more than about 10% of the criticaldensity. While it is possible that mini black holes, holes muchless massive than a solar mass, were produced in the earlyUniverse from the primeval plasma and could today providethe critical density, a plausible mechanism for producing theright number without other deleterious consequences (e.g.,black hole evaporations today producing too many -y-rays) islacking (24-26).

If flo = 1, then the question arises as to where the bulk ofthe matter is, because most dynamical measurements indi-cate fl0 0.1-0.3. This is the Q1 problem. It could be thatgalactic halos are very large and that clusters sit at the centerof gigantic distributions of dark matter, that much of thematerial exists in low-luminosity galaxies (so-called biasing),or even that it exists in a form of smoothly distributed energydensity (e.g., relativistic particles or a cosmological con-stant). In that regard one of the very nice features of neutrinodark matter is that neutrinos, owing to their large velocities,would likely remain smooth on scales out to several mega-

parsec. In any case we know that the dark matter is lesscondensed than luminous matter, indicating that it does nothave the ability to dissipate energy. This means that it couldbe in the form of particles that interact very weakly or couldbe tied up in large objects made of baryons (e.g., dead starsor dwarfs).

The Evidence for a Flat Universe!

Before pursuing the hypothesis of a flat Universe dominatedby nonbaryonic dark matter, let me quickly summarize theevidence in support of it.

(i) There is evidence for a gap between fIB and flO.(ii) A dynamical explanation for our own peculiar velocity

seems to indicate that flo is close to unity.(iii) Some kinematic measurements of Q10 based upon

galaxy counts indicate that 0l0 is close to unity (27, 28).(iv) Structure formation in a low-flO Universe is more

difficult and requires larger amplitude density perturbationsand may not be consistent with the observed isotropy of theCBR (see, e.g., refs. 29 and 30).

(v) One of the most attractive scenarios of the earlyUniverse, inflation, unambiguously predicts a flat Universe(31).

(vi) According to the Dicke-Peebles timing argument (32),if the Universe is not flat, then we must conclude that we liveat a special time when the curvature terms and matter densityterms are comparable.

Needless to say the evidence is not overwhelming; it does,however, make a case for taking the hypothesis of a flatUniverse dominated by nonbaryonic dark matter seriously.

Nonbaryonic Dark Matter

If we adopt Do = 1, then the gap between fl0 and QlB issignificant and necessitates that a new form of matter be thedominant constituent of the Universe. The point of thissection is to emphasize that particle physicists too were

pushed to nonbaryonic dark matter for reasons solely basedupon particle physics: as a consequence of addressing very

fundamental problems in particle physics, the existence ofnew particles was predicted, particles as it turned out whoserelic cosmic abundance was close to the critical density. Thiscould just be a coincidence, or it could be an important hintthat we are on the right track.The Standard Model of Particle Physics. Over the past two

decades, particle physicists have constructed a fundamentaltheory that accounts for all known phenomena at energies

below about 300 GeV (down to length scales of the order of10-16 cm). They call it the standard model (see, e.g., refs. 33and 34); mathematically, it is a non-Abelian gauge theorybased upon the group SU(3)c 0g SU(2)L ( U(l)y. The SU(3)cpart, known as quantum chromodynamics, describes thestrong interactions (the interactions that bind quarks inhadrons).§ The SU(2)L 0) U(l)y part describes the elec-troweak interactions. An important part of the standardmodel is the notion that the electromagnetic and weakinteractions are not separate phenomena, but rather differentaspects of the unified electroweak force.The fundamental particles ofthe standard models are three

families of quarks and leptons (u, d, c, t, and b quarks and ve,e-, vJL, ,u-, v, and r- leptons) and 12 gauge bosons (eightgluons, W+, W-, ZO, and the photon) that mediate thefundamental interactions. All the gauge bosons have beenseen, the top quark remains to be discovered, and there isonly indirect-but very strong indirect-evidence for theexistence of the r neutrino. All the particles participate in theelectroweak interactions; only quarks carry color and par-ticipate in the strong interactions.While the eight gluons and the photon are massless, the W+

and ZO bosons are not; this reflects the least well understoodaspect of the standard: symmetry breaking. The full symme-try of the electroweak interactions is hidden; the simplestexplanation is the Higgs mechanism and involves a new classof fundamental (scalar) particles: Higgs bosons, which havenot yet been seen. Hidden symmetry is analogous to themagnetization of a ferromagnet: at low temperatures, due tospin interactions the state of the ferromagnet with lowest freeenergy is characterized by aligned spins and a net magneti-zation and thus does not exhibit rotational invariance. Theground state of the Higgs field at low temperatures, due to itsself-interactions, breaks the symmetry of the electroweakinteractions and in so doing makes the W+ and ZO bosonsmassive (and accounts for the masses of the quarks andleptons as well). The aspects of the standard model involvingthe gauge particles and quarks and leptons have been testedto very high precision (in many cases to better than 1%); thereis no direct evidence for the Higgs mechanism, and it ispossible that something else accounts for the hidden sym-metry. One of the primary motivations for building theSuperconducting Supercollider is the elucidation of symme-try breaking (e.g., by the production of Higgs bosons).The standard model is a neat little package; in accounting

for all "known particle physics," it also explains the absenceof other phenomena. For example, why are neutrinos so light(or perhaps massless)? The SU(2)L symmetry forbids a massfor the neutrinos (in the absence of righthanded neutrinos).Why is the proton stable (or at least very long-lived)? Again,in the standard model it is not possible to have proton decaywithout violating other symmetries of the standard model.1Similar considerations forbid interactions that violate leptonnumber.New Physics Beyond the Standard Model. The tapestry of

the standard model is not without loose threads. Like thestandard cosmology it has shortcomings that point to some-thing grander; they include

(i) Quantization of charge: quarks and leptons are separatefamilies of particles, yet the charges of the quarks are to high

§The interactions between hadrons (e.g., between neutrons andprotons), which used to be referred to as the strong interactions, arenow believed to be analogous to van der Waals forces, here residualforces between color neutral objects and hence not fundamental(see, e.g., ref. 35).$This statement is true at the classical level; subtle quantum effectsassociated with instantons and the like lead to baryon-numberviolation. At temperatures ;200 GeV, these processes are probablyvery important and may play a role in explaining the origin of thebaryon asymmetry of the Universe (see, e.g., ref. 36).

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precision an integer multiple of one-third the charge of an

electron.(ii) A related issue: why are there two kinds of matter

particles (quarks and leptons) and three families of quarksand leptons? Are quarks and leptons fundamental, or are theymade of "smaller" entities?

(iii) Patchwork unification: in the standard model thefundamental forces are "patched" together, rather than trulyunified.

(iv) Parameters: the standard model has more than 20"input parameters" (sin2Ow, quark and lepton masses, mix-ing angles, etc.) that must be specified.

(v) Disparity of scales: the scale of the weak interactionGF112 300 GeV is much, much less than that of gravity,G-1/2 - 1019 GeV (the "hierarchy problem").

(vi) A related issue: how is the Higgs to remain light enoughto break the electroweak interaction at a scale of 300 GeV inthe face of quantum corrections that should drive its mass tothe highest energy scale in the theory (1019 GeV)?

(vii) The strong-CP problem: within the standard model,quantum effects (instantons again) lead to CP violation in thestrong interactions and should lead to an electric-dipolemoment for the neutron that is 109 times larger than thecurrent upper limit.

(viii) Unification ofgravity: Where and how does gravity fitin?These considerations lead most particle physicists to be-

lieve that there must be a "grander" theory. Moreover, themathematical tools at hand-non-Abelian gauge theories,supersymmetry, superstrings, to mention three-allow veryattractive and powerful theoretical speculations that addressall of these issues. These speculations lead to the predictionof new particles, some of which are stable (due to new

conservation laws) or are at least long-lived (due to theirsmall masses and/or very weak interactions). Further-andthis is the cosmological bonus-some of these new, long-lived particles have relic abundances that are comparable tothe critical density. This didn't have to be; the relic abun-dance of a particle species is determined by its mass andinteractions. This is either the big hint or the grand misdi-rection.To put things in perspective here is a very brief summary

of the extensions of the standard model and the dark-mattercandidates they predict.

(i) Peccei-Quinn (PQ) symmetry (37-40): this is a veryminimal extension of the standard model designed to solvethe strong CP problem. It is considered by many to be thebest solution and automatically arises in many supersymme-try and superstring models. Another consequence of PQsymmetry is the existence of a very long-lived, light (pseu-doscalar) particle-the axion-which is a prime dark-mattercandidate.

(ii) Majoron models (41): these are modest extensions ofthe standard model designed to accommodate neutrino massand thereby allow the three ordinary neutrino species to bedark-matter candidates.

(iii) Supersymmetry (see, e.g., ref. 42): low-energy super-symmetry is perhaps the most well-studied extension of thestandard model. Supersymmetry, the symmetry that relatesbosons and fermions, dictates that for every fermion there bea bosonic partner (and vice versa)-thereby doubling theparticle content of the standard model. First and foremost,supersymmetry addresses the hierarchy problem, "stabiliz-ing" the mass of the Higgs boson and putting scalar particleson a firm footing. It also paves the way for the unification ofgravity (when supersymmetry is gauged, it leads to generalrelativity). Supersymmetry must be a broken symmetry sincethe known particles do not have equal-mass partners; thesuperpartner masses are generically expected to be of theorder of 10-1000 GeV (of the order of the electroweak scale).

In almost all models, the lightest superpartner is stable and isa linear combination of the photino and higgsino, known asthe neutralino. The neutralino is a prime dark-matter candi-date.

(iv) Technicolor (ref. 43): this is a very attractive idea forreplacing the Higgs mechanism with physics that is analogousto that underlying the Bardeen-Cooper-Schreiffer theory ofsuperconductivity. A stronger version of Quantum Chromo-dynamics (QCD)-technicolor-leads to the formation ofbound states oftechniquarks, and these bound states play therole of the Higgs. Technicolor addresses the hierarchy prob-lem, as the mass of the Higgs is set by the energy scale atwhich technicolor becomes "strong" (just as the mass of thehadrons is set by the scale at which color becomes strong) andeliminates the need for scalar particles. However, it is anattractive idea that has been very difficult to implement: thereis currently no viable model of technicolor. Whether or notit predicts the existence of dark-matter candidates remains tobe seen.

(v) Grand unification (see, e.g., ref. 44): the basic goal ofgrand unified theories (GUTs) is to truly unify the strong,weak, and electromagnetic interactions within a single gaugegroup with one coupling constant. The simplest GUT is basedupon the gauge group SU(5) and predicts a proton lifetime of1030 yr, which, sadly, has been falsified. Other GUTs includeSO(10), E6, E8, and on and on. That unification is evenpossible-given that the coupling strengths of the differentinteractions are so different at low energies-is remarkable.In non-Abelian gauge theories, coupling strengths vary (or"run") with energy (logarithmically); the strengths of thethree known interactions seem to become equal at an energyscale of about 1016 GeV or so, which sets the scale of grandunification. Il Among other things, GUTs predict proton de-cay, neutrino masses, and the existence of superheavy mag-netic monopoles (masses of the order of the unificationscale)-the last two being dark-matter candidates. In manyGUTs, neutrino masses arise via the "see-saw mechanism"(45, 46), and min ml/Al, where ml is the charged leptonmass, and A is an energy scale associated with unification(not necessarily the unification scale itself-perhaps ordersofmagnitude smaller). This explains why neutrino masses areso very small-and in many models suggests that neutrinosmay have masses in "the electronvolt range" (anywherefrom microelectronvolts to tens of electronvolts).

(vi) Superstrings (47, 48): superstring theories unify all theforces (including gravity) in a finite quantum theory (WOW!)and are most naturally formulated in 10 dimensions (suggest-ing the existence of6 extra spatial dimensions that today mustbe compactified). The fundamental objects of the theory areone-dimensional string-like entities whose size is of the orderof 10-33 cm. The expectations for the superstring are high:ultimately, explanations for everything-quark/leptonmasses, coupling constants, the strong CP problem, thenumber of families, spartner masses, and the electroweakscale. The path has been more difficult than expected, andthere have been few definite predictions (that are not wrong).Broadly, superstring theory provides theoretical support forthe axion, supersymmetry, grand unification, and neutrinomasses-providing motivation for all the dark-matter candi-dates mentioned above.Of course, there are other ideas that I have not mentioned

because at present they do not seem viable-for example,preons, which were postulated as the constituents of quarks

"About a decade ago, the convergence of the coupling constantsoccurred in ordinary GUTs at an energy scale of about 1014 GeV;better measurements of sin2OW indicate that such a convergencedoes not occur in nonsupersymmetric GUTs, but does in super-symmetric GUTs at an energy scale of about 1016 GeV.

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and leptons, and higher-dimensional analogs of superstrings,known as membranes.Two Birds with One Stone. Particle dark matter is attractive

because new particles that owe their existence to attempts tosolve very fundamental puzzles in particle physics have arelic abundance of the order of the critical density! Histori-cally, such coincidences have been a sign that one is on theright track.**While there are now literally dozens of particle dark-matter

candidates, there are but a handful of particles whose pre-dicted existence arises due to well-motivated attempts tosolve important problems in particle physics and whose relicabundance is in the right ballpark. They are the following:

(i) The neutralino (52-54). In most supersymmetry models,the neutralino is the lightest supersymmetric partner and isstable (due to a new symmetry called R parity). Its interac-tions with ordinary matter are roughly the strength of theweak interactions, and this fact ultimately explains why itsrelic abundance is of the order of the critical density. Atpresent, supersymmetric models have many parameters thatmust be dialed in, and the mass of the neutralino is onlyknown to be somewhere between 10 GeV and 2 TeV.

(ii) The axion (55-57). PQ symmetry seems to be the bestsolution to the nagging strong-CP problem. The mass of theaxion depends upon a single parameter: the energy scale ofPQ symmetry breaking,fpQ, and ma - m2X/fpQ - 10-5 eV (1012GeV/fpQ). The strength of the axion's couplings to ordinarymatter is proportional to its mass. When the axion was firstinvented, only one scale of symmetry breaking was known:the weak scale, and there seemed to be a unique predictionfor its mass, around 200 keV. This idea was quickly falsified.It is now realized that there are likely to be many energyscales in Nature, the GUT scale, the Planck scale, theintermediate scale, and so on. The symmetry-breaking scalehas been constrained, largely by astrophysical and cosmo-logical arguments, to lie in the interval 1010 GeV !fpQ 5 1013GeV, corresponding to an axion mass in the range 10-6_10-3eV (58, 59). This also happens to be the range where the relicabundance of axions is of the order of the critical density.

(iii) The light neutrino. The neutrino exists; it comes inthree varieties; and we know its relic abundance to threesignificant figures, 113 cm-3 per species. Further, essentiallyall extensions of the standard model predict that neutrinoshave mass, and the see-saw mechanism implies masses in thegeneral range of electronvolts, give or take a factor of 103 orso.

(iv) Dark horses. There are also a few well-motivated longshots. They include the superheavy magnetic monopole: it isa generic prediction of GUTs; the only problem is its abun-dance; without inflation far too many monopoles are pro-duced; and with inflation essentially no monopoles are pro-duced (see, e.g., ref. 60). There is the supersymmetric partnerof the axion, the axino, which arises in theories with both PQsymmetry and supersymmetry (61). Its mass is expected to bein the kiloelectrovolt range, and its abundance is significantlyless than neutrinos as it decouples much earlier.Why Not Baryons or Modified Gravity? The particle dark-

matter hypothesis is a radical solution; are there otheralternatives that are less radical or perhaps more attractive?

**For a while, some believed that one could get three birds with onestone: cosmions, dark-matter particles of mass 4-10 GeV withscattering cross sections of the order of 10-35 cm2, were proposedto solve both the solar-neutrino and the dark-matter problems.This possibility is all but ruled out on both theoretical grounds-the corresponding annihilation cross section leads to a cosmionabundance that is too small in both the sun and the cosmos-andexperimental grounds-cosmions should have been detected indark-matter searches (49-51).

I think not, but to convince the reader let me mention twosuch ideas: fIB - 1 and modified Newtonian dynamics.

Primordial nucleosynthesis provides the best determina-tion of the amount of baryonic matter in the Universe,pinning down the number density of baryons to within afactor of 2. To be sure, the arguments involve assumptionsabout the Universe in the distant past. Over the years, manyhave suggested alternative scenarios of primordial nucleo-synthesis that would allow one to evade the nucleosynthesisbound and have fQB 1 (62). The most recent attemptinvolved the role of large inhomogeneities that might havebeen produced in the quark/hadron transition if it werestrongly first order. It was hoped that such inhomogeneitieswould allow QB - 1. This possibility is now "double forbid-den." As discussed at this colloquium, inhomogeneous nu-cleosynthesis allows very little, if any, loosening of thestandard bound (see, e.g., refs. 1-4); moreover, numericalsimulations of the quark/hadron transition suggest that suchinhomogeneities would not have arisen in the first place, asthe transition is at best a weakly first-order phase transitionand perhaps not a phase transition at all (more like recom-bination).

Theorists are rarely criticized for their conservatism!Moreover, it seems that every theorist worth his salt has triedto find a theory of gravity to supplant Einstein's. So onemight have expected that theorists would have embracedMilgrom's modified Newtonian dynamics (MOND) (63, 64).The basic idea ofMOND is that the form ofNewton's secondlaw is modified for accelerations less than about cHo - 10-7cm sec-2, F - ma2/cHo, thereby eliminating the need fordark matter to explain flat rotation curves. While theoristsare more than ready to consider modifications to Einstein'stheory, especially in light of superstring theory, to mosttheorists MOND looks like a nonstarter. The reason issimple: it is purely a Newtonian theory, and attempts toformulate it in terms of a relativistic field theory have beenunsuccessful. Without such a formulation, one cannot con-struct a cosmological model or evaluate its predictions for themany tests we have of relativistic theories of gravity-bending of starlight, precession of the perihelion of Mercury,gravitational redshift, radar time delay, and the myriad oftests offered by the binary pulsar. If that were not badenough, it has been argued thatMOND can be falsified on thebasis of rotation curves measured for galaxies of very differ-ent sizes (65, 66).

In sum, theorists have looked hard for other explanations;I believe that it is fair to say that the particle dark-matterexplanation is the most attractive. Whether or not it provesto be correct is another matter.

Dark-Matter Relics: Origins

Since an important motivation for particle dark matter is thefact that the relic abundance of these handful of promisingcandidates is comparable to the critical density, it is worthreviewing how a cosmological relic arises. There are severalqualitatively different mechanisms for particle dark-matterproduction in the early Universe.Thermal Relics: Hot, Warm, and Cold. Much, but not all,

of the history of the Universe is characterized by thermalequilibrium. So long as equilibrium pertains, the abundanceof a massive particle relative to photonstt is of the orderof unity for temperatures T >> m/3 and of the order of

ttThe number of particles per comoving volume, R3n, is actuallyproportional to the ratio of the particle number density to theentropy density, nls, where s X g*T3 and g* counts the effectivenumber of ultrarelativistic degrees of freedom. So long as g* isconstant, s and n, are related by a constant numerical factor, todayabout 7.04.

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(m/T)3/2 exp(-m/T) for T << m/3. For reference, thefraction of critical density contributed by a relic species is

Qh~(m ) n)1

If equilibrium were the entire story, relic abundances wouldbe far too small to be of any interest.

Consider a stable, massive particle species; its abundanceis necessarily regulated by annihilations and pair creations. Inthe expanding Universe, the temperature is decreasing, TIT

- -H; equilibrium can be maintained only if annihilationsand pair creations occur rapidly on the expansion time scale,H-1. Because of the temperature dependence of equilibriumnumber densities and of cross sections, annihilation and paircreation reactions eventually become ineffective ("freezeout"), and the abundance of a particle species relative tophotons approaches a constant value ("freezes in") (67-70).

If freeze out occurs when the species is relativistic, thenthe species' relic abundance is comparable to that ofphotons.Such a species is referred to as a hot relic; a light (mass smegaelectronvolts) neutrino species is a hot relic.On the other hand, if freeze out occurs when the species is

nonrelativistic, then its relic abundance is significantly lessthan that of photons and depends inversely upon its annihi-lation cross section (in thermal equilibrium, the annihilationrate and pair creation rate are related by detailed balance).The relic abundance is

n ln(0.01mmpj(crV)ann) 10-3

kny MMPJ(O'V)ann TOMP1(av)annwhere the second relation follows from the fact that PCRIT -

104To. This formula is quite remarkable: neglecting thelogarithmic factor and the overall numerical constant, itimplies that the fraction of critical density contributed by acold relic only depends upon its annihilation cross sectionand, further, that Ql - 1 obtains for (av)ann - 10-3/Tompi -

10-37 cm2! This is very roughly a weak-interaction crosssection (=GeV2GF2) and indicates that a stable particle withweak interactions will necessarily have a relic abundancecomparable to the critical density. A stable neutrino of massof a few gigaelectronvolts would fit the bill were it not ruledout by experiment (71-75). The neutralino fits the bill nicely,as its interactions with ordinary matter are roughly weak.The final case is warm dark matter. If a species decouples

while it is still relativistic, but very early on (T >> 1 GeV),then after it decouples its abundance relative to photons willbe diminished as various species disappear and transfer theirentropy to the photons (and other species). In this case, itsabundance is less than that of photons, but not exponentiallyless, and so closure density obtains for masses in the kiloelec-tronvolt range; plausible warm dark-matter candidates includethe axino (61) and a light gravitino (76). (This dilution by"entropy transfer" is precisely what makes the relic neutrinotemperature and abundance less than that of photons.)Skew Relics. Implicit in the previous discussion is the

assumption that the particle and its antiparticle were equallyabundant. If there is an asymmetry between particle andantiparticle and net particle number is conserved, then therelic abundance can become no smaller than the net particlenumber per photon (see, e.g., ref. 77). Provided that annihi-lations can reduce the particle's abundance to this level, therelic abundance is determined by the particle-antiparticleasymmetry.Baryons are an example of a skew relic; if not for the

asymmetry between baryons and antibaryons, the relic abun-dance of each would be about 10-18 that of photons (78). Themass density contributed by a skew relic is

fkxh2 - lo) MG [31

where qx is the particle-antiparticle asymmetry relative tophotons. A stable neutrino species with mass of the order of100 GeV and asymmetry of the order of the baryon asym-metry could provide closure density. [Neither the precisionmeasurements of the width of the ZO boson nor nucleosyn-thesis precludes such a fourth neutrino species; dark-mattersearches employing ionization detectors do unless the massexceeds a teraelectronvolt or so (79-82)].Nonthermal Relics. The magnetic monopole and axion are

examples of particles whose relic abundance involves coher-ent, nonthermal processes. Monopoles are produced as (point-like topological) defects in the GUT symmetry-breaking phasetransition (see, e.g., ref. 60). On the basis of causality con-siderations, one expects of the order of one monopole perhorizon volume (at the time of the phase transition), whichleads to a relic abundance of order n/ny - (T/mpl)3. For theGUT phase transition, T - 1015 GeV or so, which results in agross overabundance of monopoles (very crudely, "Ql -

1012"). This is the monopole problem. Inflation can solve themonopole problem provided that the GUT phase transitionoccurs before inflation, so that monopoles are diluted by themassive entropy production. This being said, it appears thatmonopoles are a terrible dark-matter candidate; however,scenarios have been proposed where their relic abundance canbe close to critical (see, e.g., ref. 60).Axions arise not only as thermal relics but also due to two

nonthermal processes, the misalignment process and thedecay of axionic strings (58, 59). For the interesting axionmasses, 10-6-10-4 eV, their thermal relic abundance cannotcome close to closure density. Since there is some disagree-ment as to the importance of the axionic string decay process(83-86) and it is impotent in an inflationary Universe, I willfocus on the misalignment process (55-57).

It is the 0 parameter of QCD that leads to the strong-CPproblem; 0 is an angular parameter that controls the strengthof the offending instanton effects. In the PQ solution, 0becomes a dynamical variable whose value is anchored at theCP-conserving value of zero by the instanton effects them-selves. However, at temperatures much greater than 1 GeV,these effects are impotent, and the value of 0 is left unde-termined by dynamical considerations. Thus, one expects thevalue of 0 to be randomly distributed in different causallyindependent regions of the Universe. When the QCD instan-ton effects do become important, 0 will in general be"misaligned" (i.e., not at 0 = 0) and will evolve toward 0 =0; as it does, 0 overshoots and is left oscillating. Thesecosmic harmonic oscillations correspond to a condensate ofvery nonrelativistic axions, whose relic density is roughly

Qlh2~= ( eV)m -1.210-' eVX [4]

The energy associated with the misalignment of 0 is con-verted into an enormous number of axions, about 109 cm-3for ma = 10-5 eV.

Signicant Other Relics. While our first interest is in eluci-dating the nature of the ubiquitous dark matter, it is possiblethat there are a number ofparticle relics in our midst. Needlessto say, a particle relic that contributes significantly less thanclosure could still be interesting-both from the point of viewof cosmology and of particle physics; moreover, it could bedetectable. The CBR provides such an example: l.y - 10-4.Until it was ruled out by a telescope search for its decays, anelectronvolt-mass axion provided another possibility (87, 88).If Nature is supersymmetric and the lightest supersymmetryparticle is stable, it is difficult to avoid a supersymmetric relic

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that contributes less than about 10-3 of closure density.Magnetic monopoles provide yet another example. If theearliest history ofthe Universe is as interesting as many think,there may be many relics whose abundance is far from criticalbut are still potentially detectable.

Truly Exotic Relics. Other more complicated explanationsfor the dark-matter problem involving early Universe relicshave been suggested. Two suggestions have been made thatwould reconcile a flat Universe with the observational datathat the amount of matter that clusters contributes only 20%or so of critical density: a "relic cosmological constant" anddark matter that decays at a modest redshift into relativisticdebris, which necessarily remains unclustered (89-92). Ineither case, dynamical measurements of fl0 would not revealthe unclustered energy density-vacuum energy or relativ-istic particles-and would yield values of the order of 20%.On the other hand, kinematic measurements could reveal thepresence of the unclustered energy density (93). In eithercase, a new cosmic coincidence comes into play: a cosmo-logical constant that becomes dynamically important in thecurrent epoch or a particle whose lifetime is comparable tothe age of the Universe.A relic cosmological constant provokes further discussion.

Historically, cosmologists have turned to the cosmologicalconstant when faced with a crisis. In the context of quantum-field theory, it is actually the absence of an enormous (A -

10122 G-1) cosmological constant associated with the zero-point energy of quantum fluctuations of the fundamentalfields that is a mystery. To confuse the situation further,several authors have argued that a Universe with a cosmo-logical constant, cold dark matter, and baryons is currentlythe best-fit Universe, in terms of the age of the Universe,dynamical measurements of flo, and the formation of struc-ture (94, 95).Other puzzles have motivated suggestions for "specialized

relics." Sciama and others (96-100) have argued for anunstable neutrino species whose radiative decays would leadto efficient reionization of the Universe. Recently, "cock-tails" of two particle relics-30% neutrinos and 70% colddark matter-have been advocated to make the cold dark-matter scenario for structure formation better agree withobservations (101-105).A New Cosmic Ratio. If the bulk of the mass density is in

the form of nonbaryonic dark matter, then cosmologists-and particle physicists-have a new dimensionless number toexplain: the ratio of ordinary matter to exotic matter. Why isit of the order of unity and not say 10-20 or 1020? The valueof this ratio has important consequences for the evolution ofthe Universe, and the fact that it is of the order of unity is atthe heart of many cosmological observations (e.g., the halo/disk conspiracy in rotation curves, the stability of galacticdisks, and even the formation of stars).Although there is presently no good explanation for why

this ratio is of the order of unity, it necessarily involvesfundamental physics. For example, consider a skew relicwhose asymmetry is comparable to the baryon asymmetry;then the ratio is just that of the exotic particle's mass to themass of a baryon. For other relics, requiring that this ratio beof the order of unity implies special relationships betweenfundamental energy scales in physics (106).

Detection

The nonbaryonic dark-matter hypothesis is a very bold one,and fortunately it is testable. While no cosmological exper-iment or observation is easy, especially the search for aparticle whose interactions could be as different as those ofan axion and a neutralino, thanks to the creative efforts ofmany, there are manifold approaches to the problem ofdetection (see, e.g., 107-109).

First, there are the direct schemes, where the halo dark-matter particles in our local neighborhood (density 5 x 10-25g.cm-3) are sought out. For axions, the approach is basedupon a very clever idea of Sikivie (110) that takes advantageof the axion's coupling to two photons. A microwave cavityis immersed in a very strong magnetic field, which causeshalo axions to be converted to photons and excites resonantmodes of the cavity; several "proof of principle experi-ments" have been built and operated, and a new generationof Sikivie detectors with sufficient sensitivity to detect haloaxions are being built (111). Neutralino detectors exploit theneutralino's roughly weak interactions with ordinary matter:when a multi-gigaelectronvolt mass neutralino scatters off anucleus, it deposits an energy oforder a kiloelectronvolt. Theannihilation cross section and elastic cross section are relatedby "crossing," and thus the scattering cross section tooshould be of the order of 10-7 cm2; this implies an event rateof the order of 1 per day per kg. A new generation oflow-background, low-threshold cryogenic detectors are be-ing developed to search for neutralinos in our halo. While themagnetic monopole must be considered a long-shot dark-matter candidate, a football field-sized detector calledMACRO is just coming on line and will achieve a sensitivityof about 10-16 cm-2 sr-1 sec-l (113).

Next, there are indirect searches, which involve seekingout the decay or annihilation products of dark-matter parti-cles. For example, dark-matter annihilations in the halo ofour galaxy can produce high-energy positrons that can bedetected (114-116). The most promising idea involves anni-hilations of dark-matter particles that accumulate in the sunand the earth (117-119); the annihilation products includehigh-energy neutrinos that can be detected in large, under-ground earth-based detectors, such as MACRO (113). Asizable portion of the neutralino parameter space can beexplored by searching for high-energy neutrinos from the sunand the earth (112).

Finally, there are numerous laboratory and astrophysicalexperiments that bear on the existence of particle darkmatter. Searches for the supersymmetric partners of theknown particles are taking place at every accelerator in theworld; the discovery ofeven one superpartner would not onlyprovide strong evidence for the existence of the neutralinobut would also help to narrow the parameter space. There area host of experiments that bear on the issue of neutrinomasses: experiments designed to measure the electron-neutrino mass, neutrino oscillation/mixing experiments, so-lar neutrino experiments, and searches for neutrinos fromtype II supernovae.

Concluding Remarks

The theorists' prejudice of a flat Universe dominated bynonbaryonic dark matter is at present just that! However, Ihope that I have convinced the reader that (i) the dark-matterquestion is a most pressing one, which now involves bothcosmologists and particle physicists; (ii) the theorists' prej-udice is well motivated by both theoretical and observationalconsiderations; and (iii) most importantly, the particle dark-matter hypothesis can and is being tested. While cosmolog-ical experiments are inherently difficult and we cannot testevery dark-matter candidate, I am optimistic. The mostpromising dark-matter candidates are detectable, and thedark-matter problem has attracted the attention of many ofthe most talented experimentalists from both cosmology andparticle physics. While this is no guarantee that we will havean answer soon, what more could one ask? And if that isn'tenough, there is the payoff: identifying and quantifying theprimary substance of the Universe and discovering "newphysics" in the process!

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This work was supported in part by the Department of Energy (atFermilab and Chicago) and by the National Aeronautics and SpaceAdministration (through NAGW-2381 at Fermilab).

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