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

Understand

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.