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Abstract:

We resurrect Eddington's proposal for the gravitational action in the presence of a cosmological constant and extend it to include matter fields. We show that the Newton-Poisson equation is modified in the presence of sources and that charged black holes show great similarities with those arising in Born-Infeld electrodynamics coupled to gravity. When we consider homogeneous and isotropic space-times we find that there is a minimum length (and maximum density) at early times, clearly pointing to an alternative theory of the Big Bang. We thus argue that the modern formulation of Eddington's theory, Born-Infeld gravity, presents us with a novel, non-singular description of the Universe.

Abstract:

A possible solution to the dark energy problem is that Einstein's theory of general relativity is modified. A suite of models have been proposed that, in general, are unable to predict the correct amount of large scale structure in the distribution of galaxies or anisotropies in the Cosmic Microwave Background. It has been argued, however, that it should be possible to constrain a general class of theories of modified gravity by focusing on properties such as the growing mode, gravitational slip and the effective, time varying Newton's constant. We show that assuming certain physical requirements such as stability, metricity and gauge invariance, it is possible to come up with consistency conditions between these various parameters. In this paper we focus on theories which have, at most, 2nd derivatives in the metric variables and find restrictions that shed light on current and future experimental constraints without having to resort to a (as yet unknown) complete theory of modified gravity. We claim that future measurements of the growth of structure on small scales (i.e. from 1-200 h^{-1} Mpc) may lead to tight constraints on both dark energy and modified theories of gravity.