The discovery of the accelerating universe in the late 1990s was a watershed moment in modern cosmology, as it indicated the presence of a fundamentally new, dominant contribution to the energy budget of the universe. Evidence for dark energy, the new component that causes the acceleration, has since become extremely strong, owing to an impressive variety of increasingly precise measurements of the expansion history and the growth of structure in the universe. Still, one of the central challenges of modern cosmology is to shed light on the physical mechanism behind the accelerating universe. In this review, we briefly summarize the developments that led to the discovery of dark energy. Next, we discuss the parametric descriptions of dark energy and the cosmological tests that allow us to better understand its nature. We then review the cosmological probes of dark energy. For each probe, we briefly discuss the physics behind it and its prospects for measuring dark energy properties. We end with a summary of the current status of dark energy research.

We present an analysis of 15 Type Ia supernovae (SNe Ia) at redshift > z 1 (9 at < < z 1.5 2.3) recently discovered in the CANDELS and CLASH Multi-Cycle Treasury programs using WFC3 on the Hubble Space Telescope. We combine these SNeIa with a new compilation of ∼1050 SNeIa, jointly calibrated and corrected for simulated survey biases to produce accurate distance measurements. We present unbiased constraints on the expansion rate at six redshifts in the range < < z 0.07 1.5 based only on this combined SNIa sample. The added leverage of our new sample at > z 1.5 leads to a factor of ∼3 improvement in the determination of the expansion rate at z=1.5, reducing its uncertainty to ∼20%, a measurement of2.69 0 0.52 0.86 . We then demonstrate that these six derived expansion rate measurements alone provide a nearly identical characterization of dark energy as the full SN sample, making them an efficient compression of the SNIa data. The new sample of SNeIa at > z 1.5 usefully distinguishes between alternative cosmological models and unmodeled evolution of the SNIa distance indicators, placing empirical limits on the latter. Finally, employing a realistic simulation of a potential Wide-Field Infrared Survey Telescope SN survey observing strategy, we forecast optimistic future constraints on the expansion rate from SNeIa.

Late-time power law expansion has been proposed as an alternative to the standard cosmological model and shown to be consistent with some low-redshift data. We test power law expansion against the standard flat ΛCDM cosmology using goodness-of-fit and model comparison criteria. We consider Type Ia supernova (SN Ia) data from two current compilations (JLA and Union2.1) along with a current set of baryon acoustic oscillation (BAO) measurements that includes the high-redshift Lyman-α forest measurements from BOSS quasars. We find that neither power law expansion nor ΛCDM is strongly preferred over the other when the SN Ia and BAO data are analyzed separately but that power law expansion is strongly disfavored by the combination. We treat the R h = ct cosmology (a constant rate of expansion) separately and find that it is conclusively disfavored by all combinations of data that include SN Ia observations and a poor overall fit when systematic errors in the SN Ia measurements are ignored, despite a recent claim to the contrary. We discuss this claim and some concerns regarding hidden model dependence in the SN Ia data.

Peculiar velocities of objects in the nearby universe are correlated due to the gravitational pull of large-scale structure. By measuring these velocities, we have a unique opportunity to test the cosmological model at the lowest redshifts. We perform this test, using current data to constrain the amplitude of the ``signal'' covariance matrix describing the velocities and their correlations. We consider a new, well-calibrated ``Supercal'' set of low-redshift SNe Ia as well as a set of distances derived from the fundamental plane relation of 6dFGS galaxies. Analyzing the SN and galaxy data separately, both results are consistent with the peculiar velocity signal of our fiducial ΛCDM model, ruling out the noise-only model with zero peculiar velocities at greater than 7σ (SNe) and 8σ (galaxies). When the two data sets are combined appropriately, the precision of the test increases slightly, resulting in a constraint on the signal amplitude of A = 1.05−0.21+0.25, where A = 1 corresponds to our fiducial model. Equivalently, we report an 11% measurement of the product of the growth rate and amplitude of mass fluctuations evaluated at zeff = 0.02, f σ8 = 0.428−0.045+0.048, valid for our fiducial ΛCDM model. We explore the robustness of the results to a number of conceivable variations in the analysis and find that individual variations shift the preferred signal amplitude by less than ∼0.5σ. We briefly discuss our Supercal SN Ia results in comparison with our previous results using the JLA compilation.