Covariant c-flation: A variational approach

Abstract

We develop an action principle to construct the dynamics that gives rise to a minimal generalization of Einstein’s equations, where the speed of light ([Formula: see text]), the gravitational constant ([Formula: see text]) and the cosmological constant ([Formula: see text]) are allowed to vary. Our construction preserves general covariance of the theory, which yields a general dynamical constraint on [Formula: see text], [Formula: see text] and [Formula: see text]. This action is general and can be applied to describe different cosmological solutions. We apply this formulation to the initial condition puzzles of the early universe and show that it generates a dynamical mechanism to obtain the homogeneous and flat universe we observe today. We rewrite the conditions necessary to solve the horizon and flatness problems in this framework, which does not necessarily lead to an accelerated expansion as in inflation. Then, we show how the dynamics of the scalar field that represents [Formula: see text] or [Formula: see text] (and [Formula: see text]) can be used to solve the problems of the early universe cosmology by means of different ways to [Formula: see text]-inflate the horizon in the early universe. By taking [Formula: see text], we show that the dynamics of the scalar field representing [Formula: see text] can be described once a potential is given.