3. DARK ENERGY AND THE ACCELERATING UNIVERSE

Recent observations of type Ia supernovae (SNe Ia) at high redshift indicate that the expansion of the Universe is accelerating [Perlmutter et al.(1999a), Riess et al.(1998a)]: although concerns about systematic errors remain, these calibrated `standard' candles appear fainter than would be expected if the expansion were slowing due to gravity. According to General Relativity, accelerated expansion requires a dominant component with effective negative pressure, w = p / < 0. Such a negative-pressure component is now generically termed Dark Energy; a cosmological constant , with p = - , is the simplest but not the only possibility. As noted in the previous Section, recent results for the CMB anisotropy, which favor a nearly flat Universe, _total = 1, coupled with a variety of observations pointing unambiguously to low values for the matter density parameter, _m = 0.3, provide independent evidence for a dark energy component with _de 0.7. Such a cosmological model, with the additional assumptions that the dark matter is (mostly) cold and that the initial perturbations are adiabatic and nearly scale-invariant (as predicted by inflation), is in excellent agreement with CMB and large-scale structure data as well.

On the other hand, the history of dark energy - more specifically the cosmological constant - is not pretty: beginning with Einstein, it has been periodically invoked by cosmologists out of desperation rather than desire, to reconcile theory with observations, and then quickly discarded when improved data or interpretation showed it was not needed. Examples include the first `age crisis' arising from Hubble's large value for the expansion rate (1929), the apparent clustering of QSOs at a particular redshift (1967), early cosmological tests which indicated a negative deceleration parameter (1974), and the second `age crisis' of the mid-1990's arising from new evidence in favor of a high value for the Hubble parameter. Despite these false starts, it seems more likely that dark energy is finally here to stay, since we now have multiple lines of evidence pointing to it.

With or without dark energy, a consistent description of the vacuum presents particle physics with a major challenge: the cosmological constant problem (see, e.g., [Weinberg(1989), Carroll et al.(1992)]). The effective energy density of the vacuum - the cosmological constant - certainly satisfies < 1, which corresponds to a vacuum energy density = / 8 G < (0.003 eV)⁴. Within the context of quantum field theory, there is as yet no understanding of why the vacuum energy density arising from zero-point fluctuations is not of order the Planck scale, M⁴_Pl, 120 orders of magnitude larger, or at least of order the supersymmetry breaking scale, M⁴_SUSY ~ TeV⁴, about 50 orders of magnitude larger. Within the context of classical field theory, there is no understanding of why the vacuum energy density is not of the order of the scale of one of the vacuum condensates, such as M⁴_GUT, M⁴_SUSY, M_W⁴ sin⁴ / (4 )² ~ (175 GeV)⁴, or f⁴ ~ (100 MeV)⁴. The observational upper bound on the vacuum density appears to require cancellation between two (or more) large numbers to very high precision. Note that this is not an argument against the cosmological constant per se, merely a statement of the fact that we do not understand why is as small as it is. Some theorists expect that whatever explains the smallness of the cosmological constant - e.g., some as yet undiscovered (or presently misunderstood) symmetry - may require it to be exactly zero, but as of yet no compelling mechanism has been proposed. This discrepancy is the most embarrassing hierarchy problem for modern particle physics theory. Moreover, the arguments above indicate that it is manifest even at low energies. It is therefore not obvious that its solution necessarily lies in unraveling physics at ultra-high energies, e.g., in string theory.

The cosmological constant problem predates the recent evidence for dark energy. However, dark energy raises a new puzzle, the so-called coincidence problem. If the dark energy satisfies _de 0.7, it implies that we are observing the Universe just at the special epoch when _m is comparable to _de, which might seem to beg for further explanation. We might rephrase these two problems as follows: (a) why is the vacuum energy density so much smaller than the fundamental scale(s) of physics? and (b) why does the dark energy density have the particular non-zero value that it does today? If the dark energy is in fact vacuum energy (i.e., a non-zero cosmological constant), then the answers to these two questions are very likely coupled; if the dark energy is not due to a pure cosmological constant, then these questions may be logically disconnected.

In recent years, a number of models in which the dark energy is dynamical, e.g., associated with a scalar field and not a fundamental cosmological constant, have been discussed (e.g., [Dolgov(1983), Ratra and Peebles(1988), Wetterich(1988), Frieman et al.(1995), Caldwell et al.(1998), Binetruy(1999), Zlatev et al.(1999), Bucher and Spergel(1999), Choi(1999), Masiero et al.(2000), Sahni and Wang(2000), Dodelson et al.(2000), Albrecht and Skordis(2000), Albrecht et al.(2001)]). These models, sometimes known as "quintessence" models, start from the assumption that questions (a) and (b) above are logically disconnected. That is, they postulate that the fundamental vacuum energy of the universe is (very nearly) zero, owing to some as yet not understood mechanism, and that this new physical mechanism `commutes' with other dynamical effects that lead to sources of energy density. This assumption implies that all such models do not address the cosmological constant problem. If this simple hypothesis is the case, then the effective vacuum energy at any epoch will be dominated by the fields with the largest potential energy which have not yet relaxed to their vacuum state. At late times, these fields must be very light.

Adopting this working hypothesis, we can immediately identify generic features which a classical model for the dark energy should have. Dark energy is most simply stored in the potential energy V() = M⁴f () of a scalar field , where M sets the characteristic height of the potential. The working hypothesis sets V(_m) = 0 at the minimum of the potential (although this assumption is not absolutely necessary); to generate a non-zero dark energy at the present epoch, must be displaced from the minimum (_{i m} as an initial condition), and to exhibit negative pressure its kinetic energy must be small compared to its potential energy. This implies that the motion of the field is still relatively damped, m = sqrt[ |V"(_i)| ] < 3H₀ = 5 × 10^-33 h eV. Second, for ~ 1 today, the potential energy density should be of order the critical density, M⁴ f() ~ 3H²₀ M²_Pl / 8, or (for f ~ 1) M 3 × 10^-3 h^1/2 eV; the resulting value of the scalar field is typically ~ M_Pl or even larger. Thus, the characteristic height and curvature of the potential are strongly constrained for a classical model of the dark energy.

This argument raises an apparent difficulty for all "quintessence" models: why is the mass scale m at least thirty orders of magnitude smaller than M and 60 orders of magnitude smaller than the characteristic field value ~ M_Pl? In quantum field theory, such ultra-low-mass scalars are not generically natural: radiative corrections generate large mass renormalizations at each order of perturbation theory. To incorporate ultra-light scalars into particle physics, their small masses should be at least `technically' natural, that is, protected by symmetries, such that when the small masses are set to zero, they cannot be generated in any order of perturbation theory, owing to the restrictive symmetry. While many phenomenological quintessence models have been proposed, with few exceptions [Frieman et al.(1995), Binetruy(1999), Choi(1999), Albrecht et al.(2001)], model builders have ignored this important issue. In many quintessence models, particularly those with "runaway" potentials (e.g., exponentials, inverse power laws), this problem is compounded by the fact that the scalar field amplitude at late times satisfies >> M<sub>Pl</sub>: the dark energy dynamics would be ruined by generically expected terms of the form <sup>4+n</sup> / M<sup>n</sup><sub>Pl</sub> unless they are highly suppressed. In addition, such `eternal' quintessence models lead to horizons, which may create difficulties for (perturbative) string theory [Banks and Dine(2001)]. On the plus side, models in which the "quintessence" field is an axion with the requisite mass scales [Frieman et al.(1995)] may perhaps arise in perturbative string theory [Choi(1999), Banks and Dine(2001)], and the radion field in brane models with large extra dimensions may also have the requisite properties for dark energy [Albrecht et al.(2001)].

Since the quintessence field must be so light, its Compton wavelength is comparable to the present Hubble radius or larger. As a result, depending on its couplings, it may mediate a new long-range force, a possibility constrained by equivalence principle experiments and astrophysical tests [Carroll(1998)]. While quintessence models have been constructed which evade these bounds [Albrecht et al.(2001)], these constraints remain an important consideration for theorists in bulding models. More sensitive equivalence principle experiments are warranted, as they will provide stronger constraints upon and (possibly) evidence for dark energy.

While "quintessence" models provide theoretical scenarios of varying plausibility for a dark energy component which differs from a cosmological constant (w = p / > - 1 if the field is rolling), the next major developments in this field will likely come from observations: progress in probing dark energy will be critical to pointing the way to theoretical understanding of it. The first challenge for the coming decade is to determine whether the dark energy equation of state parameter w is consistent with -1 (the vacuum) or not. The current constraints from SNe Ia observations (e.g., [Garnavich et al.(1998), Perlmutter et al.(1999b)]) are consistent with w = - 1, but with large uncertainties. As the errors are reduced, will w = - 1 be excluded or preferred? If the latter, i.e., dark energy consistent with vacuum energy, it will likely be difficult to make further theoretical progress without tackling the cosmological constant problem. If the former, i.e., dark energy inconsistent with vacuum energy, it would appear to point to a dynamical origin for this phenomenon. In that case, marshalling a variety of probes, including supernovae, weak lensing, cluster counting via SZ, Lyman-alpha forest clustering, and others (discussed elsewhere in these proceedings) to determine w and its possible evolution with redshift will be needed. Fortunately, it appears that the prospects for improved SNe observations and the maturation of complementary probes are quite good, and with them the prospects for determining the nature of the dark energy. As the discussion above indicates, these observations may in some sense be probing physics near the Planck scale.