Ten years after its discovery, the acceleration of the expansion of the Universe is now firmly established. The physical origin of this phenomenon, however, remains a deep mystery, linked to other important problems in physics and astronomy. At present, the simplest explanation, vacuum energy, is consistent with all extant data, but theory provides no understanding of why it should have the requisite small value. Probing the history of cosmic expansion with much greater precision (few percent vs. current 10%) offers the best hope of pointing us down the correct path to a solution. An impressive array of experiments with that aim are underway or planned, and we believe that significant progress will be made in the next fifteen years.
We conclude with our list of the ten important take-home facts about cosmic acceleration and dark energy, followed by our views on the key open issues and challenges for the future.
10.1. Take-home facts
10.1.1. STRONG EVIDENCE FOR ACCELERATED EXPANSION. Since the SN discovery of acceleration, several hundred supernovae have been observed over a broader range of redshifts, substantially strengthening the case both statistically and by reducing sources of systematic error. Further, independent of GR and based solely upon the SN Hubble diagram, there is very strong (5) evidence that the expansion of the Universe accelerated recently [Shapiro & Turner 2006].
10.1.2. DARK ENERGY AS THE CAUSE OF COSMIC ACCELERATION. Within GR, accelerated expansion cannot be explained by any known form of matter or energy but can be accommodated by a nearly smooth form of energy with large negative pressure, known as dark energy, that accounts for about 75% of the Universe.
10.1.3. INDEPENDENT EVIDENCE FOR DARK ENERGY. In the context of the cold dark matter model of structure formation, CMB and large-scale structure data provide independent evidence that the Universe contains a smooth form of energy which accounts for about 75% of the total and which only came to dominate after essentially all of the observed structure had formed. Thus, structure formation independently points to a negative-pressure (with w -1/3), dark energy accounting for the bulk of the Universe.
10.1.4. VACUUM ENERGY AS DARK ENERGY. The simplest explanation for dark energy is the energy associated with the vacuum; it is mathematically equivalent to a cosmological constant. However, all attempts to compute the vacuum energy density from the zero-point energies of all quantum fields yield a result that is many orders of magnitude too large or infinite.
10.1.5. CURRENT OBSERVATIONAL STATUS. Taken together, all the current data provide strong evidence for the existence of dark energy; they constrain the fraction of critical density contributed by dark energy, 0.76 ± 0.02, and the equation-of-state parameter, w -1 ± 0.1 (stat) ± 0.1 (sys), assuming that w is constant. This implies that the Universe began accelerating at redshift z ~ 0.4 and age t ~ 10 Gyr. These results are robust - data from any one method can be removed without compromising the constraints - and they are not substantially weakened by dropping the assumption of spatial flatness. Relaxing the assumption that w is constant and parametrizing its variation as w(z) = w0 + wa (1 - a), the current observational constraints are considerably weaker, DE 0.7 ± 0.15, w0 -1 ± 0.2, wa 0 ± 1, and provide no evidence for variation of w.
10.1.6. DARK THEORY: DARK ENERGY OR NEW GRAVITATIONAL PHYSICS? There is no compelling model for dark energy. Beyond vacuum energy, there are many intriguing ideas, including a new light scalar field and the influence of additional spatial dimensions. In many of these models, time-varying dark energy is expected. On the other hand, cosmic acceleration could be a manifestation of gravitational physics beyond GR rather than dark energy. While interesting, there is as yet no self-consistent model for the new gravitational physics that is also consistent with the large body of data that constrains theories of gravity.
10.1.7. DARK DESTINY. The destiny of the Universe depends crucially upon the nature of the dark energy. All three fates - recollapse or continued expansion with and without slowing - are possible. The existence of dark energy raises the issue of cosmic uncertainty: can we determine the mass/energy content with sufficient precision to rule out the possibility that a tiny dark energy component today may dominate in the distant future?
10.1.8. AT THE NEXUS OF MANY MYSTERIES. Because of its multiple close connections to important problems in both physics and astronomy, cosmic acceleration may be the most profound mystery in science. Its solution could shed light on or be central to unraveling other important puzzles, including the cause of cosmic inflation, the vacuum-energy problem, supersymmetry and superstrings, neutrino mass, new gravitational physics, and even dark matter.
10.1.9. THE TWO BIG QUESTIONS. Today, the two most pressing questions about cosmic acceleration are: Is dark energy something other than vacuum energy? Does GR self-consistently describe cosmic acceleration? Establishing that w ≠ -1 or that it varies with time, or that dark energy clusters, would rule out vacuum energy. Establishing that the values of w determined by the geometric and growth of structure methods are not equal could point toward a modification of gravity as the cause of accelerated expansion.
10.1.10. PROBING DARK ENERGY. An impressive array of space- and ground-based observations, using SNe, weak lensing, clusters, and baryon acoustic oscillations, are in progress or are being planned. They should determine wp, the equation-of-state parameter at the redshift where it is best determined, at the percent level and its time variation wa at the 10% level, dramatically improving our ability to discriminate between vacuum energy and something more exotic as well as testing the self-consistency of GR to explain cosmic acceleration. Laboratory and accelerator-based experiments could also shed light on dark energy.
10.2. Open issues and challenges
10.2.1. CLUSTERING OF DARK ENERGY. While vacuum energy is uniform, dynamical forms of dark energy can be inhomogeneous, making dark energy clustering a potential additional probe of dark energy. However, since dark energy is likely to cluster only weakly and on the largest scales, the prospects for clustering as a probe of dark energy are not high. Nonetheless, discovering that dark energy clusters would rule out vacuum energy. Current constraints on the clustering of dark energy are weak, and there may be better ideas about measuring dark-energy clustering.
10.2.2. DARK ENERGY AND MATTER. In scalar field models of dark energy, there is a new, very light (m H0 ~ 10-33 eV) scalar particle which can couple to matter and thereby give rise to new long-range forces with potentially observable consequences. Such an interaction could perhaps help explain the near-coincidence between the present densities of dark matter and dark energy or change the dynamics of dark matter particles, though it is constrained by astrophysical and cosmological observations to be of at most gravitational strength [Gradwohl & Frieman 1992, Carroll 1998]. A coupling to ordinary matter would have even larger observable effects and is highly constrained.
10.2.3. DESCRIBING COSMIC ACCELERATION AND DARK ENERGY. In the absence of theoretical guidance, the equation-of-state parameter w p / is a convenient way of characterizing dark energy and its effects on the expansion. One can instead take a more agnostic approach and interpret results in terms of the kinematics of the expansion or the energy density. Further, it is worth exploring improved descriptions of dark energy that both yield physical insight and are better matched to the observations.
10.2.4. SYSTEMATIC ERRORS. All of the techniques used to probe dark energy are limited by systematic errors. The sources of systematic error include: luminosity evolution and dust extinction uncertainties (for SNe Ia); shape measurement systematics, photometric redshift errors, and theoretical modeling of the matter power spectrum (for weak lensing); galaxy biasing, non-linearity, and redshift distortions (for BAO); and the uncertain relations between cluster mass and its observable proxies (for galaxy clusters). Improvements in all of these will be critical to realizing the full potential of planned observations to probe dark energy and will have beneficial effects more broadly in astronomy.
10.2.5. DARK ENERGY THEORY. The grandest challenge of all is a deeper understanding of the cause of cosmic acceleration. What is called for is not the invention of ad hoc models based upon clever ideas or new potentials, but rather a small number of theoretical models that are well motivated by fundamental physics and that make specific enough predictions to be falsified.
10.2.6. HOW MUCH IS ENOUGH? Given its profound implications and the absence of a compelling theory, dark energy is the exemplar of high-risk, high-gain science. Carrying out the most ambitious proposed dark energy projects - JDEM and LSST - to attain percent level precision will cost more than one billion dollars. While they will yield much tighter parameter constraints, there is no guarantee that they will deliver deeper understanding of dark energy. If they are able to exclude vacuum energy or demonstrate the inconsistency of GR, the implications would be revolutionary. On the other hand, if they yield results consistent with vacuum energy, it would constitute an important test of the "null hypothesis" and provide a set of cosmological parameters that will satisfy the needs for astrophysical cosmology for the foreseeable future. In this case, unless there are new theoretical developments pointing to different or more decisive probes of compelling dark energy theories, there is likely to be little enthusiasm for continuing on to even more expensive dark energy projects.
There is no doubt that pursuing the origin of cosmic acceleration will continue to be a great intellectual adventure for the next fifteen years. Even if these ambitious projects do not solve this riddle, they will at least sharpen the problem and will certainly produce a wealth of survey data that will benefit many areas of astronomy for decades to come.
We thank Andy Albrecht, Gary Bernstein, Roger Blandford, Ed Copeland, Wendy Freedman, Don Goldsmith, Wayne Hu, Rocky Kolb, Eric Linder, Adam Riess, Martin White, and Bruce Winstein for helpful comments on an earlier draft of this article. We also acknowledge the Aspen Center for Physics, where part of this review was written. This work was supported in part by the DOE at Fermilab and at the University of Chicago and by the KICP NSF Physics Frontier Center grant PHY-0114422.