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, *M*^{4}_{Pl}, 120 orders of magnitude
larger, or at least of order the supersymmetry breaking scale,
*M*^{4}_{SUSY} ~ *TeV*^{4}, 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 *M*^{4}_{GUT},
*M*^{4}_{SUSY},
*M*_{W}^{4} sin^{4}
/
(4
)^{2} ~ (175
*GeV*)^{4}, or
*f*_{}^{4}
~ (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*() =
*M*^{4}*f*
()
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})| ] < 3*H*_{0} = 5 ×
10^{-33} *h* eV. Second, for
_{} ~ 1 today,
the potential energy density should be of order the critical density,
*M*^{4}
*f*() ~
3*H*^{2}_{0}
*M*^{2}_{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*_{Pl}: the dark energy dynamics
would be ruined by generically expected terms of the form
^{4+n}
/ *M*^{n}_{Pl} 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.