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

In this paper we investigate the past evolution of an anisotropic Bianchi I universe in $R+R^2$ gravity. Using the dynamical system approach we show that there exists a new two-parameters set of solutions that includes both an isotropic “false radiation” solution and an anisotropic generalized Kasner solution, which is stable. We derive the analytic behaviour 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 checked our results.