On the covariant formalism of the effective field theory of gravity and its cosmological implications

Abstract

Following our previous work wherein the leading order effective action was computed in the covariant effective field theory of gravity, here we specialize the effective action to the FRW spacetime and obtain the effective Friedmann equations. In particular, we focus our attention on studying the cosmological implications of the non-local terms when each of them is combined with the Einstein-Hilbert action. We obtain both analytical and iterative solutions to the effective background equations in all the cases and also briefly comment on the consistency between the iterative and numerical solutions whenever possible. We find that among all the non-local terms, the imprints induced by $R\frac{1}{\square^2}R$ are very significant. Interpreting these corrections as an effective dark energy component characterized by an equation of state parameter, we find that the $R\frac{1}{\square^2}R$ correction can indeed lead to an accelerated expansion of the universe at the present epoch even in the absence of a cosmological constant. We briefly discuss some phenomenological consequences of our results.