Supersymmetry and Cosmology

Cosmology now provides unambiguous, quantitative evidence for new particle physics. I discuss the implications of cosmology for supersymmetry and vice versa. Topics include: motivations for supersymmetry; supersymmetry breaking; dark energy; freeze out and WIMPs; neutralino dark matter; cosmologically preferred regions of minimal supergravity; direct and indirect detection of neutralinos; the DAMA and HEAT signals; inflation and reheating; gravitino dark matter; Big Bang nucleosynthesis; and the cosmic microwave background. I conclude with speculations about the prospects for a microscopic description of the dark universe, stressing the necessity of diverse experiments on both sides of the particle physics/cosmology interface.


Introduction
Not long ago, particle physicists could often be heard bemoaning the lack of unambiguous, quantitative evidence for physics beyond their standard model. Those days are gone. Although the standard model of particle physics remains one of the great triumphs of modern science, it now appears that it fails at even the most basic levelproviding a reasonably complete catalog of the building blocks of our universe.
Recent cosmological measurements have pinned down the amount of baryon, matter, and dark energy in the universe. 1,2 In units of the critical density, these energy densities are Ω B = 0.044 ± 0.004 (1) Ω matter = 0.27 ± 0.04 (2) implying a non-baryonic dark matter component with where h ≃ 0.71 is the normalized Hubble expansion rate. Both the central values and uncertainties were nearly unthinkable even just a few years ago. These measurements are clear and surprisingly precise evidence that the known particles make up only a small fraction of the total energy density of the universe. Cosmology now provides overwhelming evidence for new particle physics.
At the same time, the microscopic properties of dark matter and dark energy are remarkably unconstrained by cosmological and astrophysical observations. Theoretical insights from particle physics are therefore required, both to suggest candidates for dark matter and dark energy and to identify experiments and observations that may confirm or exclude these speculations.
Weak-scale supersymmetry is at present the most well-motivated framework for new particle physics. Its particle physics motivations are numerous and are reviewed in Sec. 2. More than that, it naturally provides dark matter candidates with approximately the right relic density. This fact provides a strong, fundamental, and completely independent motivation for supersymmetric theories. For these reasons, the implications of supersymmetry for cosmology, and vice versa, merit serious consideration.
Many topics lie at the interface of particle physics and cosmology, and supersymmetry has something to say about nearly every one of them. Regrettably, spacetime constraints preclude detailed discussion of many of these topics. Although the discussion below will touch on a variety of subjects, it will focus on dark matter, where the connections between supersymmetry and cosmology are concrete and rich, the abovementioned quantitative evidence is especially tantalizing, and the role of experiments is clear and promising.
Weak-scale supersymmetry is briefly reviewed in Sec. 2 with a focus on aspects most relevant to astrophysics and cosmology. In Secs. 3 and 4 the possible roles of neutralinos and gravitinos in the early universe are described. As will be seen, their cosmological and astrophysical implications are very different; together they illustrate the wealth of possibilities in supersymmetric cosmology. I conclude in Sec. 5 with speculations about the future prospects for a microscopic understanding of the dark universe.

A New Spacetime Symmetry
Supersymmetry is an extension of the known spacetime symmetries. 3 The spacetime symmetries of rotations, boosts, and translations are generated by angular momentum operators L i , boost operators K i , and momentum operators P µ , respectively. The L and K generators form Lorentz symmetry, and all 10 generators together form Poincare symmetry. Supersymmetry is the symmetry that results when these 10 generators are further supplemented by fermionic operators Q α . It emerges naturally in string theory and, in a sense that may be made precise, 4 is the maximal possible extension of Poincare symmetry.
If a symmetry exists in nature, acting on a physical state with any generator of the symmetry gives another physical state. For example, acting on an electron with a momentum operator produces another physical state, namely, an electron translated in space or time. Spacetime symmetries leave the quantum numbers of the state invariant -in this example, the initial and final states have the same mass, electric charge, etc.
In an exactly supersymmetric world, then, acting on any physical state with the supersymmetry generator Q α produces another physical state. As with the other spacetime generators, Q α does not change the mass, electric charge, and other quantum numbers of the physical state. In contrast to the Poincare generators, however, a supersymmetric transformation changes bosons to fermions and vice versa. The basic prediction of supersymmetry is, then, that for every known particle there is another particle, its superpartner, with spin differing by 1 2 . One may show that no particle of the standard model is the superpartner of another. Supersymmetry therefore predicts a plethora of superpartners, none of which has been discovered. Mass degenerate superpartners cannot exist -they would have been discovered long ago -and so supersymmetry cannot be an exact symmetry. The only viable supersymmetric theories are therefore those with non-degenerate superpartners. This may be achieved by introducing supersymmetry-breaking contributions to superpartner masses to lift them beyond current search limits. At first sight, this would appear to be a drastic step that considerably detracts from the appeal of supersymmetry.
It turns out, however, that the main virtues of supersymmetry are preserved even if such mass terms are introduced. In addition, the possibility of supersymmetric dark matter emerges naturally and beautifully in theories with broken supersymmetry.

Supersymmetry and the Weak Scale
Once supersymmetry is broken, the mass scale for superpartners is unconstrained.
There is, however, a strong motivation for this scale to be the weak scale: the gauge hierarchy problem. In the standard model of particle physics, the classical mass of the boson mass is where the last term is the leading quantum correction, with λ the Higgs-fermion coupling. Λ is the ultraviolet cutoff of the loop integral, presumably some high scale well above the weak scale. If Λ is of the order of the Planck scale ∼ 10 19 GeV, the classical Higgs mass and its quantum correction must cancel to an unbelievable 1 part in 10 34 to produce the required weak-scale m h . This unnatural fine-tuning is the gauge hierarchy problem.
In the supersymmetric standard model, however, for every quantum correction with standard model fermions f L and f R in the loop, there are corresponding quantum corrections with superpartnersf L andf R . The physical Higgs mass then becomes where the terms quadratic in Λ cancel, leaving a term logarithmic in Λ as the leading contribution. In this case, the quantum corrections are reasonable even for very large Λ, and no fine-tuning is required.
In the case of exact supersymmetry, where mf = m f , even the logarithmically divergent term vanishes. In fact, quantum corrections to masses vanish to all orders in perturbation theory, an example of powerful non-renormalization theorems in supersymmetry. From Eq. (6), however, we see that exact mass degeneracy is not required to solve the gauge hierarchy problem. What is required is that the dimensionless couplings λ of standard model particles and their superpartners are identical, and that the superpartner masses be not too far above the weak scale (or else even the logarithmi- cally divergent term would be large compared to the weak scale, requiring another finetuned cancellation). This can be achieved simply by adding supersymmetry-breaking weak-scale masses for superpartners. In fact, other terms, such as some cubic scalar couplings, may also be added without re-introducing the fine-tuning. All such terms are called "soft," and the theory with weak-scale soft supersymmetry-breaking terms is "weak-scale supersymmetry."

The Neutral Supersymmetric Spectrum
Supersymmetric particles that are electrically neutral, and so promising dark matter candidates, are shown with their standard model partners in Fig. 2. In supersymmetric models, two Higgs doublets are required to give mass to all fermions. The two neutral Higgs bosons are H d and H u , which give mass to the down-type and up-type fermions, respectively, and each of these has a superpartner. Aside from this subtlety, the superpartner spectrum is exactly as one would expect. It consists of spin 0 sneutrinos, one for each neutrino, the spin 3 2 gravitino, and the spin 1 2 Bino, neutral Wino, and down-and up-type Higgsinos. These states have masses determined (in part) by the corresponding mass parameters listed in the top row of Fig. 2. These parameters are unknown, but are presumably of the order of the weak scale, given the motivations described above.
where c W ≡ cos θ W , s W ≡ sin θ W , and β is another unknown parameter defined by tan β ≡ H u / H d , the ratio of the up-type to down-type Higgs scalar vacuum expectation values (vevs). The mass eigenstates are called neutralinos and denoted {χ ≡ χ 1 , χ 2 , χ 3 , χ 4 }, in order of increasing mass. If M 1 ≪ M 2 , |µ|, the lightest neutralino χ has a mass of approximately M 1 and is nearly a pure Bino. However, for M 1 ∼ M 2 ∼ |µ|, χ is a mixture with significant components of each gauge eigenstate.
Finally, note that neutralinos are Majorana fermions; they are their own antiparticles. This fact has important consequences for neutralino dark matter, as will be discussed below.

R-Parity
Weak-scale superpartners solve the gauge hierarchy problem through their virtual effects. However, without additional structure, they also mediate baryon and lepton number violation at unacceptable levels. For example, proton decay p → π 0 e + may be mediated by a squark as shown in Fig. 3.
An elegant way to forbid this decay is to impose the conservation of R-parity R p ≡ (−1) 3(B−L)+2S , where B, L, and S are baryon number, lepton number, and spin, respectively. All standard model particles have R p = 1, and all superpartners have R p = −1. R-parity conservation implies ΠR p = 1 at each vertex, and so both vertices in Fig. 3 are forbidden. Proton decay may be eliminated without R-parity conservation, for example, by forbidding B or L violation, but not both. However, in these cases, the non-vanishing R-parity violating couplings are typically subject to stringent constraints from other processes, requiring some alternative explanation.
An immediate consequence of R-parity conservation is that the lightest supersymmetric particle (LSP) cannot decay to standard model particles and is therefore stable.
Particle physics constraints therefore naturally suggest a symmetry that provides a new stable particle that may contribute significantly to the present energy density of the universe.

Supersymmetry Breaking and Dark Energy
Given R-parity conservation, the identity of the LSP has great cosmological importance. The gauge hierarchy problem is no help in identifying the LSP, as it may be solved with any superpartner masses, provided they are all of the order of the weak scale. What is required is an understanding of supersymmetry breaking, which governs the soft supersymmetry-breaking terms and the superpartner spectrum.
The topic of supersymmetry breaking is technical and large. However, the most popular models have "hidden sector" supersymmetry breaking, and their essential features may be understood by analogy to electroweak symmetry breaking in the standard model. In simple cases where only one non-zero F vev develops, the gravitino mass is where M * ≡ (8πG N ) −1/2 ≃ 2.4 × 10 18 GeV is the reduced Planck mass. The standard model superpartner masses are determined through the mediating interactions by terms such as where c ij and c a are constants,f i and λ a are superpartners of standard model fermions and gauge bosons, respectively, and M m is the mass scale of the mediating interactions.
When Z → F , these terms become mass terms for sfermions and gauginos. Assuming In supergravity models, the mediating interactions are gravitational, and so M m ∼ M * . We then have and √ F ∼ √ M weak M * ∼ 10 10 GeV. In such models with "high-scale" supersymmetry breaking, the gravitino or any standard model superpartner could in principle be the LSP. In contrast, in "low-scale" supersymmetry breaking models with M m ≪ M * , such as gauge-mediated supersymmetry breaking models, √ F ∼ √ M weak M m ≪ 10 10 GeV, and the gravitino is necessarily the LSP.
As with electroweak symmetry breaking, the dynamics of supersymmetry breaking contributes to the energy density of the vacuum, that is, to dark energy. In nonsupersymmetric theories, the vacuum energy density is presumably naturally Λ ∼ M 4 * instead of its measured value ∼ meV 4 , a discrepancy of 10 120 . This is the cosmological constant problem. In supersymmetric theories, the vacuum energy density is naturally F 2 . For high-scale supersymmetry breaking, one finds Λ ∼ M 2 weak M 2 * , reducing the discrepancy to 10 90 . Lowering the supersymmetry breaking scale as much as possible to F ∼ M 2 weak gives Λ ∼ M 4 weak , still a factor of 10 60 too big. Supersymmetry therefore eliminates from 1/4 to 1/2 of the fine-tuning in the cosmological constant, a truly underwhelming achievement. One must look deeper for insights about dark energy and a solution to the cosmological constant problem.

Minimal Supergravity
To obtain detailed information regarding the superpartner spectrum, one must turn to specific models. These are motivated by the expectation that the weak-scale supersymmetric theory is derived from a more fundamental framework, such as a grand unified theory or string theory, at smaller length scales. This more fundamental theory should be highly structured for at least two reasons. First, unstructured theories lead to violations of low energy constraints, such as bounds on flavor-changing neutral currents and CP-violation in the kaon system and in electric dipole moments. Second, the gauge coupling constants unify at high energies in supersymmetric theories, 5 and a more fundamental theory should explain this.
From this viewpoint, the many parameters of weak-scale supersymmetry should be derived from a few parameters defined at smaller length scales through renormalization group evolution. Minimal supergravity, 6,7,8,9,10 the canonical model for studies of supersymmetry phenomenology and cosmology, is defined by 5 parameters: where the most important parameters are the universal scalar mass m 0 and the universal gaugino mass M 1/2 , both defined at the grand unified scale M GUT ≃ 2 × 10 16 GeV. In fact, there is a sixth free parameter, the gravitino mass As noted in Sec. 2.5, the gravitino may naturally be the LSP. It may play an important cosmological role, as we will see in Sec. 4. For now, however, we follow most of the literature and assume the gravitino is heavy and so irrelevant for most discussions.
The renormalization group evolution of supersymmetry parameters is shown in lustrates several key features that hold more generally. First, as superpartner masses evolve from M GUT to M weak , gauge couplings increase these parameters, while Yukawa couplings decrease them. At the weak scale, colored particles are therefore expected to be heavy, and unlikely to be the LSP. The Bino is typically the lightest gaugino, and the right-handed sleptons (more specifically, the right-handed stauτ R ) are typically the lightest scalars.
Second, the mass parameter m 2 Hu is typically driven negative by the large top Yukawa coupling. This is a requirement for electroweak symmetry breaking: at treelevel, minimization of the electroweak potential at the weak scale requires is either the the lightest neutralino χ or the right-handed stauτ R . In the χ LSP case, where are also shown. The neutralino is nearly pure Bino in much of parameter space, but may have a significant Higgsino mixture for m 0 > ∼ 1 TeV, where Eq. (15) implies |µ| ∼ M 1 . There are, of course, many other models besides minimal supergravity. Phenomena that do not occur in minimal supergravity may very well occur or even be generic in other supersymmetric frameworks. On the other hand, if one looks hard enough, minimal supergravity contains a wide variety of dark matter possibilities, and it will serve as a useful framework for illustrating many points below.

Summary
• Supersymmetry is a new spacetime symmetry that predicts the existence of a new boson for every known fermion, and a new fermion for every known boson.
• The gauge hierarchy problem may be solved by supersymmetry, but requires that all superpartners have masses at the weak scale.
• The introduction of superpartners at the weak scale mediates proton decay at unacceptably large rates unless some symmetry is imposed. An elegant solution, R-parity conservation, implies that the LSP is stable. Electrically neutral superpartners, such as the neutralino and gravitino, are therefore promising dark matter candidates.
• The superpartner masses depend on how supersymmetry is broken. In models with high-scale supersymmetry breaking, such as supergravity, the gravitino may or may not be the LSP; in models with low-scale supersymmetry breaking, the gravitino is the LSP.
• Among standard model superpartners, the lightest neutralino naturally emerges as the dark matter candidate from the simple high energy framework of minimal supergravity.
• Supersymmetry reduces fine tuning in the cosmological constant from 1 part in 10 120 to 1 part in 10 60 to 10 90 , and so does not provide much insight into the problem of dark energy.

Neutralino Cosmology
Given the motivations described in Sec. 2 for stable neutralino LSPs, it is natural to consider the possibility that neutralinos are the dark matter. 13,14,15 In this section, we review the general formalism for calculating thermal relic densities and its implications for neutralinos and supersymmetry. We then describe a few of the more promising methods for detecting neutralino dark matter.

Freeze Out and WIMPs
Dark matter may be produced in a simple and predictive manner as a thermal relic of the Big Bang. The very early universe is a very simple place -all particles are in thermal equilibrium. As the universe cools and expands, however, interaction rates become too low to maintain this equilibrium, and so particles "freeze out." Unstable particles that freeze out disappear from the universe. However, the number of stable particles asymptotically approaches a non-vanishing constant, and this, their thermal relic density, survives to the present day.
This process is described quantitatively by the Boltzmann equation where n is the number density of the dark matter particle χ, H is the Hubble parameter, σ A v is the thermally averaged annihilation cross section, and n eq is the χ number density in thermal equilibrium. On the right-hand side of Eq. (18), the first term accounts for dilution from expansion. The n 2 term arises from processes χχ → ff that destroy χ particles, and the n 2 eq term arises from the reverse process ff → χχ, which creates χ particles.
It is convenient to change variables from time to temperature, where m is the χ mass, and to replace the number density by the co-moving number where s is the entropy density. The expansion of the universe has no effect on Y , because s scales inversely with the volume of the universe when entropy is conserved.
In terms of these new variables, the Boltzmann equation is In this form, it is clear that before freeze out, when the annihilation rate is large compared with the expansion rate, Y tracks its equilibrium value Y eq . After freeze out, Y approaches a constant. This constant is determined by the annihilation cross section σ A v . The larger this cross section, the longer Y follows its exponentially decreasing equilibrium value, and the lower the thermal relic density. This behavior is shown in Let us now consider WIMPs -weakly interacting massive particles with mass and annihilation cross section set by the weak scale: Neglecting numerical factors, n eq ∼ (mT ) 3/2 e −m/T for a non-relativistic particle, and H ∼ T 2 /M * . From these relations, we find that WIMPs freeze out when Since 1 2 mv 2 = 3 2 T , WIMPs freeze out with velocity v ∼ 0.3. One might think that, since the number density of a particle falls exponentially once the temperature drops below its mass, freeze out should occur at T ∼ m. This is not the case. Because gravity is weak and M * is large, the expansion rate is extremely slow, and freeze out occurs much later than one might naively expect. For a m ∼ 300 GeV particle, freeze out occurs not at T ∼ 300 GeV and time t ∼ 10 −12 s, but rather at temperature T ∼ 10 GeV and time t ∼ 10 −8 s.
With a little more work, 17 one can find not just the freeze out time, but also the freeze out density A typical weak cross section is corresponding to a thermal relic density of Ωh 2 ∼ 0.1. WIMPs therefore naturally have thermal relic densities of the observed magnitude. The analysis above has ignored many numerical factors, and the thermal relic density may vary by as much as a few orders of magnitude. Nevertheless, in conjunction with the other strong motivations for new physics at the weak scale, this coincidence is an important hint that the problems of electroweak symmetry breaking and dark matter may be intimately related.

Thermal Relic Density
We now want to apply the general formalism above to the specific case of neutralinos. This is complicated by the fact that neutralinos may annihilate to many final states: ff , W + W − , ZZ, Zh, hh, and states including the heavy Higgs bosons H, A, and H ± .
Many processes contribute to each of these final states, and nearly every supersymmetry parameter makes an appearance in at least one process. The full set of annihilation diagrams is discussed in Ref. 18. Codes to calculate the relic density are publicly available. 19 Given this complicated picture, it is not surprising that there are a variety of ways to achieve the desired relic density for neutralino dark matter. What is surprising, however, is that many of these different ways may be found in minimal supergravity, provided one looks hard enough. We will therefore consider various regions of minimal supergravity parameter space where qualitatively distinct mechanisms lead to neutralino dark matter with the desired thermal relic density.

Bulk Region
As evident from Fig. 6, the LSP is a Bino-like neutralino in much of minimal supergravity parameter space. It is useful, therefore, to begin by considering the pure Bino limit. In this case, all processes with final state gauge bosons vanish. This follows from supersymmetry and the absence of 3-gauge boson vertices involving the hypercharge gauge boson.
The process χχ → ff through a t-channel sfermion does not vanish in the Bino limit. This process is the first shown in Fig. 8. This reaction has an interesting structure.
Recall that neutralinos are Majorana fermions. If the initial state neutralinos are in an S-wave state, the Pauli exclusion principle implies that the initial state is CP-odd, with total spin S = 0 and total angular momentum J = 0. If the neutralinos are gauginos, the vertices preserve chirality, and so the final state ff has spin S = 1. This is compatible with J = 0 only with a mass insertion on the fermion line. This process is therefore either P -wave-suppressed (by a factor v 2 ∼ 0.1) or chirality suppressed (by a factor m f /M W ). In fact, this conclusion holds also for mixed gaugino-Higgsino neutralinos and for all other processes contributing to the ff final state. 18 (It also has important implications for indirect detection. See Sec. 3.4.) The region of minimal supergravity parameter space with a Bino-like neutralino where χχ → ff yields the right relic density is the (m 0 , M 1/2 ) ∼ (100 GeV, 200 GeV) region shown in Fig. 9. It is called the "bulk region," as, in the past, there was a wide range of parameters with m 0 , M 1/2 < ∼ 300 GeV that predicted dark matter within the observed range. The dark matter energy density has by now become so tightly constrained, however, that the "bulk region" has now been reduced to a thin ribbon of acceptable parameter space.
Moving from the bulk region by increasing m 0 and keeping all other parameters fixed, one finds too much dark matter. This behavior is evident in Fig. 9 and not difficult to understand: in the bulk region, a large sfermion mass suppresses σ A v , which implies a large Ω DM . In fact, sfermion masses not far above current bounds are required to offset the P -wave suppression of the annihilation cross section. This is an interesting fact -cosmology seemingly provides an upper bound on superpartner masses! If this were true, one could replace subjective naturalness arguments by the fact that the universe cannot be overclosed to provide upper bounds on superpartner masses.
Unfortunately, this line of reasoning is not airtight even in the constrained framework of minimal supergravity. The discussion above assumes that χχ → ff is the only annihilation channel. In fact, however, for non-Bino-like neutralinos, there are many other contributions. Exactly this possibility is realized in the focus point region, which we describe next.
In passing, it is important to note that the bulk region, although the most straightforward and natural in many respects, is also severely constrained by other data. The existence of a light superpartner spectrum in the bulk region implies a light Higgs boson mass, and typically significant deviations in low energy observables such as b → sγ and (g − 2) µ . Current bounds on the Higgs boson mass, as well as concordance between experiments and standard model predictions for b → sγ and (possibly) (g − 2) µ , therefore disfavor this region, as can be seen in Fig. 9. For this reason, it is well worth considering other possibilities, including the three we now describe.

Focus Point Region
As can be seen in Fig. 6, a Bino-like LSP is not a definitive prediction of minimal supergravity. For large scalar mass parameter m 0 , the Higgsino mass parameter |µ| drops to accommodate electroweak symmetry breaking, as required by Eq. (15). The LSP then becomes a gaugino-Higgsino mixture. The region where this happens is called the focus point region, a name derived from peculiar properties of the renormalization group equations which suggest that large scalar masses do not necessarily imply fine-tuning. 21,22,23 In the focus point region, the first diagram of Fig. 8 is suppressed by very heavy

A Funnel Region
A third possibility realized in minimal supergravity is that the dark matter annihilates to fermion pairs through an s-channel pole. The potentially dominant process is through the A Higgs boson (the last diagram of Fig. 8), as the A is CP-odd, and so may couple to an initial S-wave state. This process is efficient when 2m χ ≈ m A . In fact, the A resonance may be broad, extending the region of parameter space over which this process is important.
The A resonance region occurs in minimal supergravity for tan β > ∼ 40 24,25 and is shown in Fig. 11. Note that the resonance is so efficient that the relic density may be reduced too much. The desired relic density is therefore obtained when the process is near resonance, but not exactly on it.

Co-annihilation Region
Finally, the desired neutralino relic density may be obtained even if χχ annihilation is inefficient if there are other particles present in significant numbers when the LSP freezes out. The neutralino density may then be brought down through co-annihilation with the other species. 26,27 Naively, the presence of other particles requires that they be mass degenerate with the neutralino to within the temperature at freeze out, T ≈ m χ /30. In fact, co-annihilation may be so enhanced relative to the P -wave-suppressed χχ annihilation cross section that co-annihilation may be important even with mass splittings much larger than T .
The co-annihilation possibility is realized in minimal supergravity along theτ LSP χ LSP border. (See Fig. 9.) Processes such as χτ → τ * → τ γ are not P -wave suppressed, and so enhance the χχ annihilation rate substantially. There is therefore a narrow finger extending up to masses m χ ∼ 600 GeV with acceptable neutralino thermal relic densities.

Direct Detection
If dark matter is composed of neutralinos, it may be detected directly, that is, by looking for signals associated with its scattering in ordinary matter. Dark matter velocity and spatial distributions are rather poorly known and are an important source of uncertainty. 28,29,30,31,32 A common assumption is that dark matter has a local energy density of ρ χ = 0.3 GeV/cm 3 with a velocity distribution characterized by a velocity v ≈ 220 km/s. Normalizing to these values, the neutralino flux is Such values therefore predict a substantial flux of halo neutralinos in detectors here on Earth.
The maximal recoil energy from a WIMP scattering off a nucleus N is With such low energies, elastic scattering is the most promising signal at present, although the possibility of detecting inelastic scattering has also been discussed. As we will see below, event rates predicted by supersymmetry are at most a few per kilogram per day. Neutralino dark matter therefore poses a serious experimental challenge, requiring detectors sensitive to extremely rare events with low recoil energies.
Neutralino-nucleus interactions take place at the parton level through neutralinoquark interactions, such as those in Fig. 12. Because neutralinos now have velocities v ∼ 10 −3 , we may take the non-relativistic limit for these scattering amplitudes. In this limit, only two types of neutralino-quark couplings are non-vanishing. 33 The interaction Lagrangian may be parameterized as Feynman diagrams contributing to χq → χq scattering.
The first term is the spin-dependent coupling, as it reduces to S χ · S N in the nonrelativistic limit. The second is the spin-independent coupling. All of the supersymmetry model dependence is contained in the parameters α SD q and α SI q . The t-channel Higgs exchange diagram of Fig. 12 contributes solely to α SI q , while the s-channel squark diagram contributes to both α SD q and α SI q . For neutralinos scattering off protons, the spin-dependent coupling is dominant.
However, the spin-independent coupling is coherent and so greatly enhanced for heavy nuclei, a fact successfully exploited by current experiments. As a result, spinindependent direct detection is currently the most promising approach for neutralino dark matter, and we focus on this below.
Given the parameters α SI q , the spin-independent cross section for χN scattering is where is the reduced mass of the χ-N system, Z and A are the atomic number and weight of the nucleus, respectively, and are constants quantifying what fraction of the nucleon's mass is carried by quark q. For the light quarks, 34 f p Tu = 0.020 ± 0.004 f n Tu = 0.014 ± 0.003 The contribution from neutralino-gluon couplings mediated by heavy quark loops may be included by taking . 35 The number of dark matter scattering events is where N N is the number of target nuclei, T is the experiment's running time, M D is the mass of the detector, and the proton scattering cross section σ p has been normalized to a near-maximal supersymmetric value. This is a discouragingly low event rate. However, for a detector with a fixed mass, this rate is proportional to µ 2 N A. For heavy nuclei with A ∼ m χ /m p , the event rate is enhanced by a factor of ∼ A 3 , providing the strong enhancement noted above.
Comparisons between theory and experiment are typically made by converting all results to proton scattering cross sections. In Fig. 13, minimal supergravity predictions for spin-independent cross sections are given. These vary by several orders of magnitude. In the stau co-annihilation region, these cross sections can be small, as the neutralino is Bino-like, suppressing the Higgs diagram, and squarks can be quite heavy, suppressing the squark diagram. However, in the focus point region, the neutralino is a gaugino-Higgsino mixture, and the Higgs diagram is large. Current and projected experimental sensitivities are also shown in Fig. 13. Current experiments are just now probing the interesting parameter region for supersymmetry, but future searches will provide stringent tests of some of the more promising minimal supergravity predictions.
The DAMA collaboration has reported evidence for direct detection of dark matter from annual modulation in scattering rates. 37 The favored dark matter mass and proton spin-independent cross section are shown in Fig. 14 It is worth noting, however, that the current results bode well for the future, as many well-motivated supersymmetry models predict cross sections not far from current sensitivities. * Recent data from CDMS in the Soudan mine has pushed the discrepancy to even greater levels. 40

Indirect Detection
After freeze out, dark matter pair annihilation becomes greatly suppressed. However, after the creation of structure in the universe, dark matter annihilation in overdense regions of the universe may again become significant. Dark matter may therefore be detected indirectly: pairs of dark matter particles annihilate somewhere, producing something, which is detected somehow. There are a large number of possibilities. Below we briefly discuss three of the more promising signals.

Positrons
Dark matter in our galactic halo may annihilate to positrons, which may be detected The positron background is most likely to be composed of secondaries produced in the interactions of cosmic ray nuclei with interstellar gas, and is expected to fall as ∼ E −3.1 e + . At energies below 10 GeV, there are also large uncertainties in the background. 51,52 The most promising signal is therefore hard positrons from χχ annihilation.
Unfortunately, the monoenergetic signal χχ → e + e − is extremely suppressed. As noted above, χχ → ff is either P -wave suppressed or chirality suppressed. At present times, as opposed to during freeze out, P -wave suppression is especially severe, since v 2 ∼ 10 −6 , and so direct annihilation to positrons is effectively absent. † The positron signal therefore results from processes such as χχ → W + W − followed by W + → e + ν, and is a continuum, not a line, at the source.
To obtain the positron energy distribution we would observe, the source energy distribution must be propagated through the halo to us. The resulting differential positron flux is 52 dΦ where ρ χ is the local neutralino mass density, the sum is over all annihilation channels, and B i e + is the branching fraction to positrons in channel i. The source function f (E 0 ) gives the initial positron energy distribution from neutralino annihilation. G(E 0 , E) is the Green's function describing positron propagation in the galaxy 60 and contains all the halo model dependence.
Three sample positron spectra are given in Fig. 15. For all of them, E 2 dΦ/dE peaks at energies E ∼ m χ /2. These signals are all well below background. However, a smooth halo distribution has been assumed. For clumpy halos, which are well within the realm of possibility, the signal may be enhanced significantly. In the next few years, both PAMELA, a satellite detector, and AMS-02, an experiment to be placed on the International Space Station, will provide precision probes of the positron spectrum.
These experiments and other recently completed experiments are listed in Table 1.
Finally, the High Energy Antimatter Telescope (HEAT) experiment, a balloonborne magnetic spectrometer, has found evidence for an excess of positrons at energy ∼ 8 GeV in data from 1994/95 61,62 and 2000. 63 The observed bump in the positron fraction N e + /(N e + + N e − ) is not naturally obtained by neutralino dark matter for two reasons. First, as noted above, for a smooth halo, the annihilation cross sections that produce the desired relic density predict positron fluxes that are far too low to explain the observed excess. In principle, this objection may be overcome by a sufficiently † Note that this suppression is rather special, in that it follows from the Majorana nature of neutralinos; it is absent for other types of dark matter, such as dark matter with spin 1. 58,59  Two "best fit" results from Ref. 65 are shown in Fig. 16. In this study, the ignorance of subhalo structure is parameterized by a constant B s , an overall normalization factor that enhances the positron flux relative to what would be expected for a smooth halo.
As can be seen in Fig. 16, both spectra give improved fits to the data. They require

Photons
Dark matter in the galactic center may annihilate to photons, which can be detected in atmospheric Cherenkov telescopes on the ground, or in space-based detectors. 47,68,69,70,71,72,73,74 (Photons from the galactic halo, 75,76 or even from extra-galactic sources 77 have also been considered.) The main source of photons is from cascade decays of other primary annihilation products. A line source from loop-mediated processes such as χχ → γγ 78,79,80 and χχ → γZ 81 is possible, 70 but is typically highly suppressed. 82 The differential photon flux along a direction that forms an angle ψ with respect to the direction of the galactic center is where the sum is over all annihilation channels, ρ is the neutralino mass density, and the integral is along the line of sight. All of the halo model dependence is isolated in The integrated photon signal for 4 representative minimal supergravity models is given in Fig. 17. A moderate halo profile is assumed. Experiments sensitive to such photon fluxes are listed in Table 2, and their sensitivities are given in Fig. 17.

Neutrinos
When neutralinos pass through astrophysical objects, they may be slowed below escape velocity by elastic scattering. Once captured, they then settle to the center, where  sections, but also on χN scattering, which determines the neutralino capture rate in the Sun and Earth.
As with positrons, χχ → νν is helicity-suppressed, and so neutrinos are produced only in the decays of primary annihilation products. Typical neutrino energies are then E ν ∼ 1 2 m χ to 1 3 m χ , with the most energetic spectra resulting from W W , ZZ, and, to a lesser extent, ττ . After propagating to the Earth's surface, neutrinos are detected through their charged-current interactions. The most promising signal is from upwardgoing muon neutrinos that convert to muons in the surrounding rock, water, or ice, producing through-going muons in detectors. The detection rate for such neutrinos is greatly enhanced for high energy neutrinos, as both the charged-current cross section and the muon range are proportional to E ν .
The most promising source of neutrinos is the core of the Sun. Muon flux rates from the Sun are presented in Fig. 18. Fluxes as large as 1000 km −2 s −1 are possible.
Past, present, and future neutrino telescopes and their properties are listed in Table 3. Comparing Fig. 18 with Table 3, we find that present limits do not significantly constrain the minimal supergravity parameter space. However, given that the effective area of neutrino telescope experiments is expected to increase by 10 to 100 in the next few years, muon fluxes of order 10-100 km −2 yr −1 may be within reach.

Summary
Neutralinos are excellent dark matter candidates. The lightest neutralino emerges naturally as the lightest supersymmetric particle and is stable in simple supersymmetric models. In addition, the neutralino is non-baryonic, cold, and weakly-interacting, and so has all the right properties to be dark matter, and its thermal relic density is naturally in the desired range.
Current bounds on Ω DM are already highly constraining. Although these constraints do not provide useful upper bounds on supersymmetric particle masses, they do restrict supersymmetric parameter space. In minimal supergravity, the cosmologically preferred regions of parameter space include the bulk, focus point, A funnel, and stau coannihilation regions.
Neutralinos may be detected either directly through their interactions with ordinary matter or indirectly through their annihilation decay products. Null results from direct  Fig. 19.
The sensitivities assumed, and experiments likely to achieve these sensitivities in the near future, are listed in Table 4.
Several interesting features are apparent. First, traditional particle physics and dark matter searches, particularly indirect detection experiments, are highly complementary.
Second, at least one dark matter experiment is predicted to see a signal in almost all of the cosmologically preferred region. This illustration is in the context of minimal supergravity, but can be expected to hold more generally. The prospects for neutralino dark matter discovery are therefore promising.

Gravitino Cosmology
In Sec. 3, we largely ignored the gravitino. In this Section, we will rectify this omission. Although gravitino interactions are highly suppressed, gravitinos may have im-

Gravitino Properties
The properties of gravitinos may be systematically derived by supersymmetrizing the standard model coupled to gravity. Here we will be content with highlighting the main results.
In an exactly supersymmetric theory, the gravitino is a massless spin 3/2 particle with two degrees of freedom. Once supersymmetry is broken, the gravitino eats a spin 1/2 fermion, the Goldstino of supersymmetry breaking, and becomes a massive spin 3/2 particle with four degrees of freedom. As noted in Sec. 2.5, the resulting gravitino Table 4. Constraints on supersymmetric models used in Fig. 19. We also list experiments likely to reach these sensitivities in the near future. From Ref. 95 where M * ≡ (8πG N ) −1/2 ≃ 2.4 × 10 18 GeV is the reduced Planck mass. Gravitinos couple standard model particles to their superpartners through gravitino-gaugino-gauge boson interactions and gravitino-sfermion-fermion interactions In models with high-scale supersymmetry breaking, such as conventional super- We will focus on theories with high-scale supersymmetry breaking in the following discussion. Note, however, that in theories with low-scale supersymmetry breaking, the gravitino may be much lighter, for example, as light as ∼ eV in some simple gauge-mediated supersymmetry breaking models. The gravitino's interactions through its Goldstino components may also be much stronger, suppressed by F/M weak rather than M * . For a summary of gravitino cosmology in such scenarios, see Ref. 99.

Thermal Relic Density
If gravitinos are to play a cosmological role, we must first identify their production mechanism. There are a number of possibilities. Given our discussion of the neutralino thermal relic density in Sec. 3, a natural starting place is to consider gravitino production as a result of freeze out from thermal equilibrium. At present, the gravitino coupling E/M * is a huge suppression. However, if we extrapolate back to very early times with temperatures T ∼ M * , even gravitational couplings were strong, and gravitinos were in thermal equilibrium, with nG = n eq . Once the temperature drops below the Planck scale, however, gravitinos quickly decouple with the number density appropriate for relativistic particles. Following decoupling, their number density then satisfies nG ∝ R −3 ∝ T 3 . This has the same scaling behavior as the background photon number density, however, and so we expect roughly similar number densities now.
If such gravitinos are stable, they could be dark matter. In fact, the first supersymmetric dark matter candidate proposed was the gravitino. 100 However, the overclosure bound implies This is not surprising -relic neutrinos have a similar density, and the overclosure bound on their mass is similar.
On the other hand, gravitinos may be unstable. 101 This may be because R-parity is broken, or because the gravitino is not the LSP. In this case, there is no bound from overclosure, but there are still constraints. In particular, the gravitino's decay products will destroy the successful predictions of BBN for light element abundances if the decay takes place after BBN. In the case where decay to a lighter supersymmetric particle is possible, we can estimate the gravitino lifetime to be Requiring gravitino decays to be completed before BBN at t ∼ 1 s implies 101 mG > ∼ 10 TeV .
In both cases, the required masses are incompatible with the most natural expectations of conventional supergravity theories. Gravitinos may, however, be a significant component of dark matter if they are stable with mass ∼ keV. Such masses are possible in low-scale supersymmetry breaking scenarios, given an appropriately chosen supersymmetry-breaking scale F .

Production during Reheating
In the context of inflation, the gravitino production scenario of Sec. 4.2 is rather unnatural. Between the time when T ∼ M * and now, we expect the universe to inflate, which would dilute any gravitino relic thermal density. Inflation does provide another source for gravitinos, however. Specifically, following inflation, we expect an era of reheating, during which the energy of the inflaton potential is transferred to standard model particles and superpartners, creating a hot thermal bath in which gravitinos may be produced. 102,103,104,105,106 After reheating, the universe is characterized by three hierarchically separated rates: the interaction rate of standard model particles and their superpartners with each other, σ SM n; the expansion rate, H; and the rate of interactions involving one gravitino, σGn.
Here n is the number density of standard model particles. After reheating, the universe is expected to have a temperature well below the Planck scale, but still well above standard model masses. These rates may then be estimated by dimensional analysis, and we find The picture that emerges, then, is that after reheating, there is a thermal bath of standard model particles and their superpartners. Occasionally these interact to produce a gravitino through interactions like gg →gG. The produced gravitinos then propagate through the universe essentially without interacting. If they are stable, as we will assume throughout this section, they contribute to the present dark matter density.
To determine the gravitino abundance, we turn once again to the Boltzmann equa- In this case, the source term n 2 eq arises from interactions such as gg →gG. In contrast to our previous application of the Boltzmann equation in Sec. 3.1, however, here the n 2 sink term, originating from interactions such asgG → gg, is negligible. Changing variables as before with t → T and n → Y ≡ n/s, we find process i

Production from Late Decays
A third mechanism for gravitino production is through the cascade decays of other supersymmetric particles. If the gravitino is not the LSP, cascade decays will bypass the gravitino, given its highly suppressed couplings. However, as discussed in Sec. 2.5, the gravitino may be the LSP, even in high-scale supersymmetry breaking models. If the gravitino is the LSP, all cascades will ultimately end in a gravitino.
An alternative gravitino dark matter scenario is therefore the following. 108,109 Assume that the gravitino is the LSP and stable. To separate this scenario from the previous two, assume that inflation dilutes the primordial gravitino density and the universe reheats to a temperature low enough that gravitino production is negligible.
Because the gravitino couples only gravitationally with all interactions suppressed by the Planck scale, it plays no role in the thermodynamics of the early universe. The next-to-lightest supersymmetric particle (NLSP) therefore freezes out as usual; if it is weakly-interacting, its relic density will be near the desired value. However, much later, the NLSP decays to the gravitino LSP. The gravitino therefore becomes dark matter with relic density ΩG = mG m NLSP Ω NLSP .
The gravitino and NLSP masses are naturally of the same order in theories with highscale supersymmetry breaking. Gravitino LSPs may therefore form a significant relic component of our universe, inheriting the desired relic density from WIMP decay.
In contrast to the previous two production mechanisms, the desired relic density is achieved naturally without the introduction of new energy scales.
Given our discussion in Sec. 4.2, the decay time of Eq. (46), well after BBN, should be of concern. In the present case, the decaying particle is a WIMP and so has a density far below that of a relativistic particle. (Recall Fig. 7.) However, one must check to see if the light element abundances are greatly perturbed. In fact, for some weak-scale NLSP and gravitino masses they are, and for some they aren't. 108,109 We discuss this below, along with other constraints on this scenario.
Models with weak-scale extra dimensions also provide a similar dark matter particle in the form of Kaluza-Klein gravitons, 108,114 with Kaluza-Klein gauge bosons or leptons playing the role of the decaying WIMP. 58,59 Because such dark matter candidates naturally preserve the WIMP relic abundance, but have interactions that are weaker than weak, they have been named superweakly-interacting massive particles, or "superWIMPs." ‡ We see now that our discussion in Sec. 3 of WIMP dark matter was only valid for the "half" of parameter space where m 3/2 > m LSP . When the gravitino is the LSP, there are number of new implications of supersymmetry for cosmology. For example, the "τ LSP" region is no longer excluded by searches for charged dark matter, 108,109,115,116 as theτ is no longer stable, but only metastable. There is therefore the possibility of stable heavy charged particles appearing in collider detectors. 117,118 Further, regions with too much dark matter are no longer excluded, because the gravitino dark matter density is reduced by mG/m NLSP relative to the NLSP density. As we will discuss below, the late decays producing gravitinos may have detectable consequences for BBN and the cosmic microwave background. Astrophysical signatures in the diffuse photon spectrum, 108 the ionization of the universe, 119 and the suppression of small scale structure 120 are also interesting possibilities.

Detection
If gravitinos are the dark matter, all direct and indirect searches for dark matter are hopeless, because all interaction cross sections and annihilation rates are suppressed by the Planck scale. Instead, one must turn to finding evidence for gravitino production in the early universe. In the case of gravitinos produced at T ∼ M * or during reheating, ‡ A different dark matter candidate that also predicts late decays is axinos. 110,111,112,113 the relevant physics is at such high energy scales that signals are absent, or at least require strong theoretical assumptions. In the case of production by late decays, however, there are several possible early universe signals. We consider a few of these in this Section.

Energy Release
If gravitinos are produced by late decays, the relevant reaction is NLSP →G + S, where S denotes one or more standard model particles. Because the gravitino is essentially invisible, the observable consequences rely on finding signals of S production in the early universe. Signals from late decays have been considered in Refs. 121,122,123,124,125,126,127,128,129,130,131. In principle, the strength of these signals depends on what S is and its initial energy distribution. It turns out, however, that most signals depend only on the time of energy release, that is, the NLSP's lifetime τ , and the average total electromagnetic or hadronic energy released in NLSP decay.
Here we will consider two possible NLSPs: the photino and the stau. In the photino case, In the limit ∆m ≡ mγ − mG ≪ mG, the decay lifetime is independent of the overall superpartner mass scale. For the stau case, In the limit ∆m ≡ mτ − mG ≪ mG, the decay lifetime is The electromagnetic energy release is conveniently written in terms of where ε EM is the initial electromagnetic energy released in each NLSP decay, and Y NLSP ≡ n NLSP /n BG γ is the NLSP number density before they decay, normalized to the number density of background photons n BG γ = 2ζ(3)T 3 /π 2 . We define hadronic energy release similarly as ζ had ≡ ε had Y NLSP .
NLSP velocities are negligible when they decay, and so the potentially visible energy is For the photino case, S = γ. At leading order, all of the initial photon energy is deposited in an electromagnetic shower, and so For the stau case, where the range in ε EM results from the possible variation in electromagnetic energy from π ± and ν decay products. The precise value of ε EM is in principle calculable once the stau's chirality and mass, and the superWIMP mass, are specified. However, as the possible variation in ε EM is not great relative to other effects, we will simply present results below for the representative value of ε EM = 1 2 E τ . The lifetimes and energy releases in the photino and stau NLSP scenarios are given in Fig. 22 for a range of (m NLSP , ∆m).
Such values have testable implications, as we now discuss.

Big Bang Nucleosynthesis
Big Bang nucleosynthesis predicts primordial light element abundances in terms of one free parameter, the baryon-to-photon ratio η ≡ n B /n γ . At present, the observed D, 4 He, 3 He, and 7 Li abundances may be accommodated for baryon-to-photon ratios in the range 132 η 10 ≡ η/10 −10 = 2.6 − 6.2 .
(See Fig. 23.) In light of the difficulty of making precise theoretical predictions and reducing (or even estimating) systematic uncertainties in the observations, this consistency is a well-known triumph of standard Big Bang cosmology. there is no fine-tuned cancellation of unrelated effects, it prohibits significant entropy production between the times of BBN and decoupling. Second, the CMB measurement supports determinations of η from D, already considered by many to be the most reliable BBN baryometer. It suggests that if D and another BBN baryometer disagree, the "problem" lies with the other light element abundance -either its systematic uncertainties have been underestimated, or its value is modified by new astrophysics or particle physics. At present BBN predicts a 7 Li abundance significantly greater observed. This disagreement may therefore provide specific evidence for late-decaying particles in general, and gravitino dark matter in particular.
Given the overall success of BBN, the first implication for new physics is that it For theτ NLSP scenario, we assume ε EM = 1 2 E τ . BBN constraints exclude the shaded regions. 127 The best fit region with (τ, ζ EM ) ∼ (3 × 10 6 s, 10 −9 GeV), where 7 Li is reduced to observed levels by late decays of NLSPs to gravitinos, is given by the circle. The 7 Li anomaly discussed above may be taken as evidence for new physics, however. To improve the agreement of observations and BBN predictions, it is necessary to destroy 7 Li without harming the concordance between CMB and other BBN determinations of η. This may be accomplished for (τ, ζ EM ) ∼ (3 × 10 6 s, 10 −9 GeV). 127 This "best fit" point is marked in Fig. 24. The amount of energy release is determined by the requirement that 7 Li be reduced to observed levels without being completely destroyed -one cannot therefore be too far from the " 7 Li low" region. In addition, one cannot destroy or create too much of the other elements. These are balanced in the channel of Fig. 24 between the "low D" and "high D" regions, and the requirement that the electromagnetic energy that destroys 7 Li not disturb the D abundance specifies the preferred decay time τ ∼ 3 × 10 6 s.
Without theoretical guidance, this scenario for resolving the 7 Li abundance is rather fine-tuned: possible decay times and energy releases span tens of orders of magnitude, and there is no motivation for the specific range of parameters required to resolve BBN discrepancies. In the superWIMP scenario, however, both τ and ζ EM are specified: the decay time is necessarily that of a gravitational decay of a weak-scale mass particle, leading to Eq. (46), and the energy release is determined by the requirement that su-perWIMPs be the dark matter, leading to Eq. (56). Remarkably, these values coincide with the best fit values for τ and ζ EM . More quantitatively, we note that the grids of predictions for theγ andτ scenarios given in Fig. 24 cover the best fit region. Current discrepancies in BBN light element abundances may therefore be naturally explained by gravitino dark matter.
This tentative evidence may be reinforced or disfavored in a number of ways.
Improvements in the BBN observations discussed above may show if the 7 Li abundance is truly below predictions. In addition, measurements of 6 Li/H and 6 Li/ 7 Li may constrain astrophysical depletion of 7 Li and may also provide additional evidence for late decaying particles in the best fit region. 124,136,125,127,137 Finally, if the best fit region is indeed realized by NLSP →G decays, there are a number of other testable implications for cosmology and particle physics. We discuss one of these in the following section. Additional discussion, including diffuse photon signals, the implications of hadronic energy release, and novel collider analyses, may be found in Refs. 108,109,138,139,140,141,142,143.

The Cosmic Microwave Background
The injection of electromagnetic energy may also distort the frequency dependence of the CMB black body radiation. For the decay times of interest, with redshifts z ∼ 10 5 − 10 7 , the resulting photons interact efficiently through γe − → γe − , but photon number is conserved, since double Compton scattering γe − → γγe − and thermal bremsstrahlung eX → eXγ, where X is an ion, are inefficient. The spectrum therefore relaxes to statistical but not thermodynamic equilibrium, resulting in a Bose-Einstein distribution with chemical potential µ = 0. where In Fig. 25 we show contours of chemical potential µ. The current bound is µ < 9 × 10 −5 . 145, 132 We see that, although there are at present no indications of deviations from black body, current limits are already sensitive to the superWIMP scenario, and particularly to regions favored by the BBN considerations described in Sec. 4.5.2. In the future, the Diffuse Microwave Emission Survey (DIMES) may improve sensitivities to µ ≈ 2 × 10 −6 . 146 DIMES will therefore probe further into superWIMP parameter space, and will effectively probe all of the favored region where the 7 Li underabundance is explained by gravitino dark matter.

Summary
• The gravitino mass is determined by the scale of supersymmetry breaking and may be anywhere in the range from eV to TeV. In supergravity theories, its mass is at the weak scale and its couplings are suppressed by the Planck scale, and so extremely weak.
• If gravitinos are produced as a thermal relic, their mass is bounded by overclosure to be mG < ∼ keV if they are stable, and by BBN to be mG > ∼ 10 TeV if they are unstable.
• Gravitinos may be produced after inflation during reheating. For stable weakscale gravitinos, overclosure places an upper bound on the reheat temperature of the order of 10 10 GeV.
• Weak-scale gravitinos may also be produced in NLSP decays at time t ∼ 10 4 − 10 8 s. In this case, gravitinos may be dark matter, naturally inheriting the desired relic density. Gravitino dark matter is undetectable by conventional direct and indirect dark matter searches, but may be discovered through its imprint on early universe signals, such as BBN and the CMB.

Prospects
We have now discussed a wide variety of cosmological implications of supersymmetry.
If discoveries are made in astrophysical and cosmological observations, what are the prospects for determining if this new physics is supersymmetry? Put more generally, what are the prospects for a microscopic understanding of the dark universe? Such questions are grand, and their answers speculative. Nevertheless, some lessons may be drawn even now. As we will see, even in the best of cases, we will need diverse experiments from both particle physics and cosmology to explore this frontier.

The Particle Physics/Cosmology Interface
As a case study, let us confine our discussion to one topic: neutralino dark matter. We assume that non-baryonic dark matter is in fact neutralinos. If this is so, what are the prospects for establishing this, and what tools will we need?
It is first important to recognize the limitations of both cosmology and particle physics when taken separately: • Cosmological observations and astrophysical experiments cannot discover supersymmetry. As noted in Sec. 1, cosmological data leaves the properties of dark matter largely unconstrained. If dark matter is discovered in direct or indirect detection experiments, its mass and interaction strengths will be bounded but only very roughly at first. (For example, the region favored by the DAMA signal spans factors of a few in both mass and interaction strength; see Fig. 14.) These constraints will be sharpened by follow-up experiments. However, the microscopic implications of such experiments are clouded by significant astrophysical ambiguities, such as the dark matter velocity distribution, halo profiles, etc. Even with signals in a variety of direct and indirect detection experiments, it is unlikely that dark matter properties will be constrained enough to differentiate supersymmetry from other reasonable possibilities.
• Particle experiments cannot discover dark matter. If weak-scale superpartners exist, particle colliders will almost certainly be able to discover at least some of them. However, even if they find all of them, the dark matter candidate will most likely appear only as missing energy and momentum. Furthermore, collider experiments can only test the stability of such particles up to lifetimes of ∼ 10 −7 s.
As we have seen in Sec. 4, lifetimes of a year or more are perfectly natural in wellmotivated models of new physics. The conclusion that a particle seen in collider experiments is the dark matter therefore requires an unjustified extrapolation of 24 orders of magnitude in the particle's lifetime.
Through the combination of both approaches, however, it is possible that a cohesive and compelling theory of dark matter will emerge. A schematic picture of the combined investigation of neutralino dark matter is given in Fig. 26. 147 Working from the bottom, cosmological observations have already determined the relic density with some precision. Future observations, such as by the Planck satellite, 148 are likely to reduce uncertainties in the relic density determination to the 1% level, given now standard cosmological assumptions. Astrophysical experiments may also detect dark matter either directly through its interactions with ordinary matter or indirectly through its annihilation decay products. Such data, combined with astrophysical inputs such as the dark matter halo profile and local density, will provide information about the strength of χN scattering and χχ annihilation.  parameters will, in principle, fix the neutralino's thermal relic density, the χN scattering cross section, and the neutralino pair annihilation rates. Completion of this program at a high level of precision, followed by detailed comparison with the measured relic density and detection rates from cosmology and astrophysics will provide a great deal of information about the suitability of neutralinos as dark matter candidates.

The Role of Colliders
Clearly data from particle colliders will be required to identify neutralino dark matter.
The requirements for colliders depend sensitively on what scenario is realized in nature.
As examples, consider some of the cosmologically preferred regions of minimal supergravity discussed in Sec. 3.2. In the bulk region, one must verify that the neutralino is Bino-like and must determine the masses of sfermions that appear in the t-channel annihilation diagrams. In the focus point region, the neutralino's gaugino-ness must be precisely measured, whereas in the A funnel region, a high precision measurement of m A −2m χ is critical. Finally, for the co-annihilation region, there is extreme sensitivity to theτ -χ mass splitting. Measurements below the GeV level are required to accurately determine the predicted thermal relic density.
Let us consider the bulk region scenario in more detail. Not all sfermion masses give the dominant contribution, since these have the largest hypercharge Y and the annihilation diagram is proportional to Y 4 . In such cases, measurements of ml R and lower bounds on left-handed slepton and squark masses will provide a reasonable starting point.
The possibility of doing this at the LHC has been considered in Ref. 149. In much of the bulk region, the cascade decayq L →χ 0 2 q →l R lq → l + l −χ0 1 q is open. Kinematic endpoints may then be used to determine thel R andχ 0 1 masses precisely. Assuming that the lightest neutralino is Bino-like, one may then estimate the relic density, keeping onlỹ l R exchange diagrams. As shown in Fig. 27, this provides an estimate accurate to about ∼ 20% in minimal supergravity. Following this, one would then need to determine the gaugino-ness of the lightest neutralino and set lower bounds on the other sfermion masses.
At a linear collider, one may establish that the new particles being produced are supersymmetric by measuring their dimensionless couplings. One may then go on to determine the gaugino-ness of the LSP in a model-independent manner. For example, the cross section σ(e + e − R →χ +χ− ) nearly vanishes for gaugino-like charginos. It therefore provides a sensitive measure of chargino gaugino-ness. (See Fig. 28.) Com- bined with kinematic measurements of the chargino mass, the parameters M 2 and µ may be measured precisely. Further measurements can use these results to pinpoint M 1 and tan β, and thereby the gaugino-ness of the LSP. Precisions of ∼ 1% or better are possible, translating into predictions for relic densities and dark matter cross sections that will match the precision expected from cosmological data.

Synthesis
If the relic density and interaction strengths as determined by astrophysics and cosmology agree with the predictions of particle physics with high precision, this agreement will provide strong evidence that the dark matter is in fact supersymmetric. It will imply that we understand the history of the universe back to the freeze out temperature ∼ 10 GeV, or times t ∼ 10 −8 s. Recall that our current knowledge of the history of the universe is on sure footing only back to Big Bang nucleosynthesis at temperatures of ∼ MeV, or times t ∼ 1 s. Dark matter studies could therefore provide the necessary evidence to push back our knowledge of the universe another 8 orders of magnitude in time, a formidable achievement.
On the other hand, the determinations of relic density and dark matter interaction strengths by particle physics and cosmology may not agree. Progress then has many possible paths. If the disparity is great, one might look to other dark matter candidates, such as the axion 151,152,153 or other supersymmetric possibilities. 154,155,156,110,111,112 If the relic density determinations are reasonably close, one might explore the possibility that the neutralino is not stable, but deposits much of its relic density in a gravitino LSP, as discussed in Sec. 4.4.
Alternatively, one might look to non-standard cosmologies for a resolution. The identification of the thermal relic density with the present day cold dark matter density is subject to cosmological assumptions. The calculation of the thermal relic density assumes that the dominant source of dark matter is from dark matter particles falling out of thermal equilibrium. It is possible, however, that the bulk of the dark matter is created not through thermal equilibrium and freeze out, but through the out-of-equilibrium decay of a supermassive particle. The actual relic density would then be greater than the thermal relic density. The thermal relic density calculation also assumes that nothing unusual happens once the dark matter is produced at temperatures of T ∼ O(10) GeV.
Large entropy production by late-decaying particles may dilute calculated relic densities. In this case, the actual relic density would be less than the naive thermal relic density. The bottom line is that the cold dark matter density obtained following the path from the bottom of Fig. 26 need not coincide with the thermal relic density obtained by following the path from the top. Instead, discrepancies might provide new insights into the history of our universe.
In a similar vein, the neutralino-nucleon cross sections need not match the dark matter detection rates. As stressed above, this correspondence requires astrophysical assumptions. The uncertainties and problems associated with these issues have been discussed extensively. 28,29,31,32 It is possible, however, that the relic densities, as determined independently by particle physics and cosmology, agree to 1%, but the detection rates differ. One would then be confident that neutralinos are the dark matter and particle physics uncertainties would be eliminated, allowing detection experiments to probe astrophysics. For example, direct detection rates would then provide information about the local dark matter density and velocity distributions, and indirect detection rates would provide information about halo profiles. The synergy between cosmology and particle physics would then truly come full circle.

Summary
A microscopic understanding of the dark universe is a challenging goal. As an example, we have focused here on prospects for a fundamental description of dark matter.
Cosmological measurements, although able to bound total energy densities, cannot tell us much about the dark matter's microscopic properties. On the other hand, particle physics experiments may produce dark matter and may measure its properties rather precisely, but cannot never establish its stability on cosmological time scales. It is only through the combination of approaches in particle physics, astrophysics, and cosmology that the identity of dark matter will be uncovered. The task requires many diverse experiments, and will likely take decades to complete. Nevertheless, if any of the connections between the weak scale and cosmology described here are realized in nature, one would be hard-pressed to envision a more exciting era of discovery than the coming years.