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In 1998, two teams studying distant Type Ia supernovae presented independent evidence that the expansion of the Universe is speeding up [Riess et al. 1998, Perlmutter et al. 1999]. Since Hubble, cosmologists had been trying to measure the slowing of the expansion due to gravity; so expected was slow-down that the parameter used to quantify the second derivative of the expansion, q0, was called the deceleration parameter [Sandage 1962]. The discovery of cosmic acceleration is arguably one of the most important developments in modern cosmology.

The ready acceptance of the supernova results was not a foregone conclusion. The cosmological constant, the simplest explanation of accelerated expansion, had a checkered history, having been invoked and subsequently withdrawn several times before. This time, however, subsequent observations, including more detailed studies of supernovae and independent evidence from clusters of galaxies, large-scale structure, and the cosmic microwave background (CMB), confirmed and firmly established this remarkable finding.

The physical origin of cosmic acceleration remains a deep mystery. According to General Relativity (GR), if the Universe is filled with ordinary matter or radiation, the two known constituents of the Universe, gravity should lead to a slowing of the expansion. Since the expansion is speeding up, we are faced with two possibilities, either of which would have profound implications for our understanding of the cosmos and of the laws of physics. The first is that 75% of the energy density of the Universe exists in a new form with large negative pressure, called dark energy. The other possibility is that General Relativity breaks down on cosmological scales and must be replaced with a more complete theory of gravity.

Through a tangled history, dark energy is tied to Einstein's cosmological constant, Lambda. Einstein introduced Lambda into the field equations of General Relativity in order to produce a static, finite cosmological model [Einstein 1917]. With the discovery of the expansion of the Universe, the rationale for the cosmological constant evaporated. Fifty years later, [Zel'dovich 1968] realized that Lambda, mathematically equivalent to the stress-energy of empty space—the vacuum—cannot simply be dismissed. In quantum field theory, the vacuum state is filled with virtual particles, and their effects have been measured in the shifts of atomic lines and in particle masses. However, estimates for the energy density associated with the quantum vacuum are at least 60 orders of magnitude too large and in some cases infinite, a major embarrassment known as the cosmological constant problem [Weinberg 1989].

Despite the troubled history of Lambda, the observational evidence for cosmic acceleration was quickly embraced by cosmologists, because it provided the missing element needed to complete the current cosmological model. In this model, the Universe is spatially flat and accelerating; composed of baryons, dark matter, and dark energy; underwent a hot, dense, early phase of expansion that produced the light elements via big bang nucleosynthesis and the CMB radiation; and experienced a much earlier epoch of accelerated expansion, known as inflation, which produced density perturbations from quantum fluctuations, leaving an imprint on the CMB anisotropy and leading by gravitational instability to the formation of large-scale structure.

The current cosmological model also raises deep issues, from the origin of the expansion itself and the nature of dark matter to the genesis of baryons and the cause of accelerated expansion. Of all these, the mystery of cosmic acceleration may be the richest, with broad connections to other important questions in cosmology and in particle physics. For example, the destiny of the Universe is tied to understanding dark energy; primordial inflation also involves accelerated expansion and its cause may be related; dark matter and dark energy could be linked; cosmic acceleration could provide a key to finding a successor to Einstein's theory of gravity; the smallness of the energy density of the quantum vacuum might reveal something about supersymmetry or even superstring theory; and the cause of cosmic acceleration could give rise to new long-range forces or be related to the smallness of neutrino masses.

This review is organized into three parts. The first part is devoted to Context: in Section 2 we briefly review the Friedmann-Robertson-Walker (FRW) cosmology, the framework for understanding how observational probes of dark energy work. Section 3 provides the historical context, from Einstein's introduction of the cosmological constant to the supernova discovery. Part Two covers Current Status: in Section 4, we review the web of observational evidence that firmly establishes accelerated expansion. Section 5 summarizes current theoretical approaches to accelerated expansion and dark energy, including discussion of the cosmological constant problem, models of dark energy, and modified gravity, while Section 6 focuses on different phenomenological descriptions of dark energy and their relative merits. Part Three addresses The Future: Section 7 discusses the observational techniques that will be used to probe dark energy, primarily supernovae, weak lensing, large-scale structure, and clusters. In Section 8, we discuss specific projects aimed at constraining dark energy planned for the next fifteen years which have the potential to provide insights into the origin of cosmic acceleration. The connection between the future of the Universe and dark energy is the topic of Section 9. We summarize in Section 10, framing the two big questions about cosmic acceleration where progress should be made in the next fifteen years - Is dark energy something other than vacuum energy? Does General Relativity self-consistently describe cosmic acceleration? - and discussing what we believe are the most important open issues.

Our goal is to broadly review cosmic acceleration for the astronomy community. A number of useful reviews target different aspects of the subject, including: theory [Copeland, Sami & Tsujikawa 2006, Padmanabhan 2003]; cosmology [Peebles & Ratra 2003]; the physics of cosmic acceleration [Uzan 2007]; probes of dark energy [Huterer & Turner 2001]; dark energy reconstruction [Sahni & Starobinsky 2006]; dynamics of dark energy models [Linder 2007]; the cosmological constant [Carroll, Press & Turner 1992, Carroll 2001], and the cosmological constant problem [Weinberg 1989].

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