Anisotropic cosmological solutions in $$R + R^2$$ R+R2 gravity

Abstract

Abstract In this paper we investigate the past evolution of an anisotropic Bianchi I universe in $$R+R^2$$ R+R2 gravity. Using the dynamical system approach we show that there exists a new two-parameter set of solutions that includes both an isotropic “false radiation” solution and an anisotropic generalized Kasner solution, which is stable. We derive the analytic behavior of the shear from a specific property of f(R) gravity and the analytic asymptotic form of the Ricci scalar when approaching the initial singularity. Finally, we numerically check our results.