Isotropisation of Quadratic Gravity: Scalar and Tensor Components

Abstract

It is believed that soon after the Planck era, spacetime should have a semi-classical nature. Therefore, it is unavoidable to modify the theory of General Relativity or look for alternative theories of gravitation. An interesting possibility found in the literature considers two geometric counter-terms to regularize the divergences of the effective action. These counter-terms are responsible for a higher order derivative metric theory of gravitation. In the present letter we investigate how isotropisation occurs. For this reason a single solution is chosen throughout this article. We obtain perturbatively, by two different methods, that the tensor and scalar components emerge naturally during the isotropisation process. In this sense our result provides a numerical example to Stelle's well known result on classical gravity with higher derivates. Our entire analysis is restricted to the particular Bianchi type $I$ case.