Quadratic gravity and cosmological solutions

Abstract

Near a spacetime singularity, one expects a semiclassical behavior of quantized fields over a classical geometrical background. In this context, gravity is not quantized, being a pure classical field coupled to another quantized field. To obtain a finite value for the effective action at the one-loop level, Einstein’s actionmust be modified to an action quadratic in curvature. The intention of this work is to write down the classical field equations for a spatially homogenous geometry in expansion-normalized variables. The advantage of using these variables is that, in some sense, they give stronger criteria for isotropization. The solutions are analyzed with and without the cosmological constant, for an empty Universe, with zero energy-momentumsource. The formalism is applied to the Bianchi I case, which should reflect the behavior of all Bianchi types if the 3-curvature becomes irrelevant. It is shown in a stronger sense that isotropization occurs. An anisotropic Universe is likely for a very primordial Universe.