We show that cosmic acceleration can arise due to very tiny corrections to the usual gravitational action of general relativity, of the form R Ϫn with nϾ0. This model eliminates the need for a nonzero cosmological constant or any other form of dark energy, attributing a purely gravitational origin to the acceleration of the universe.

We consider general curvature-invariant modifications of the Einstein-Hilbert action that become important only in regions of extremely low space-time curvature. We investigate the far future evolution of the universe in such models, examining the possibilities for cosmic acceleration and other ultimate destinies. The models generically possess de Sitter space as an unstable solution and exhibit an interesting set of attractor solutions which, in some cases, provide alternatives to dark energy models. *

We discuss chaotic inflation in the context of a phenomenological modification of gravity inspired by the Chaplygin gas equation of state. We find that all observational constraints can be satisfied provided that the Chaplygin scale and the inflaton mass are smaller than 6.9 × 10 −3 M and 4.7 × 10 −6 M , respectively, where M 2 ≡ (8πG) −1 is the reduced Planck mass.PACS numbers: 98.80.Cq, 98.65.Es

In the context of (4 + d)-dimensional general relativity, we propose an inflationary scenario wherein 3 spatial dimensions grow large, while d extra dimensions remain small. Our model requires that a self-interacting d-form acquire a vacuum expectation value along the extra dimensions.This causes 3 spatial dimensions to inflate, whilst keeping the size of the extra dimensions nearly constant. We do not require an additional stabilization mechanism for the radion, as stable solutions exist for flat, and for negatively curved compact extra dimensions. From a four-dimensional perspective, the radion does not couple to the inflaton; and, the small amplitude of the CMB temperature anisotropies arises from an exponential suppression of fluctuations, due to the higherdimensional origin of the inflaton. The mechanism triggering the end of inflation is responsible, both, for heating the universe, and for avoiding violations of the equivalence principle due to coupling between the radion and matter.