Modifications of general relativity provide an alternative explanation to dark energy for the observed acceleration of the universe. We review recent developments in modified gravity theories, focusing on higher dimensional approaches and chameleon/f
(R) theories. We classify these models in terms of the screening mechanisms that enable such theories to approach general relativity on small scales (and thus satisfy solar system constraints). We describe general features of the modified Friedman equation in such theories. The second half of this review describes experimental tests of gravity in light of the new theoretical approaches. We summarize the high precision tests of gravity on laboratory and solar system scales. We describe in some detail tests on astrophysical scales ranging from ~kpc (galaxy scales) to ~Gpc (large-scale structure). These tests rely on the growth and inter-relationship of perturbations in the metric potentials, density and velocity fields which can be measured using gravitational lensing, galaxy cluster abundances, galaxy clustering and the Integrated Sachs-Wolfe effect. A robust way to interpret observations is by constraining effective parameters, such as the ratio of the two metric potentials. Currently tests of gravity on astrophysical scales are in the early stages --- we summarize these tests and discuss the interesting prospects for new tests in the coming decade.
We present a case that current observations may already indicate new gravitational physics on cosmological scales. The excess of power seen in the Lyman-alpha forest and small-scale CMB experiments, the anomalously large bulk flows seen both in pecul
iar velocity surveys and in kinetic SZ, and the higher ISW cross-correlation all indicate that structure may be more evolved than expected from LCDM. We argue that these observations find a natural explanation in models with infinite-volume (or, at least, cosmological-size) extra dimensions, where the graviton is a resonance with a tiny width. The longitudinal mode of the graviton mediates an extra scalar force which speeds up structure formation at late times, thereby accounting for the above anomalies. The required graviton Compton wavelength is relatively small compared to the present Hubble radius, of order 300-600 Mpc. Moreover, with certain assumptions about the behavior of the longitudinal mode on super-Hubble scales, our modified gravity framework can also alleviate the tension with the low quadrupole and the peculiar vanishing of the CMB correlation function on large angular scales, seen both in COBE and WMAP. This relies on a novel mechanism that cancels a late-time ISW contribution against the primordial Sachs-Wolfe amplitude.
