Beyond Einstein's General Relativity

Abstract: Modern astrophysical and cosmological models are plagued with two severe theoretical difficulties, namely, the dark energy and the dark matter problems. Relative to the former, high-precision observational data have confirmed with startling evidence that the Universe is undergoing a phase of accelerated expansion. This phase, one of the most important and challenging current problems in cosmology, represents a new imbalance in the governing gravitational equations. Several candidates, responsible for this expansion, have been proposed in the literature, in particular, dark energy models and modified gravity, amongst others. Outstanding questions are related to the nature of this so-called "dark energy" that is driving the acceleration of the universe, and whether it is due to the vacuum energy or a dynamical field. On the other hand, the late-time cosmic acceleration may be due to modifications of General Relativity, which introduce new degrees of freedom to the gravitational sector itself. We analyze some of the modified theories of gravity that address these intriguing and exciting problems facing modern physics, and explore the foundations of gravitation theory, essential for the construction of modified theories of gravity.