Nonlinear anisotropy growth in Bianchi-I spacetime in metric $f(R)$ cosmology

The present work is related to anisotropic cosmological evolution in metric $f(R)$ theory of gravity. The initial part of the paper develops the general cosmological dynamics of homogeneous anisotropic Bianchi-I spacetime in $f(R)$ cosmology. The anisotropic spacetime is pervaded by a barotropic fluid which has isotropic pressure. The paper predicts nonlinear growth of anisotropy in such spacetimes. In the later part of the paper we display the predictive power of the nonlinear differential equation responsible for the cosmological anisotropy growth in various relevant cases. We present the exact solutions of anisotropy growth in Starobinsky inflation driven by quadratic gravity and exponential gravity theory. Semi-analytical results are presented for the contraction phase in quadratic gravity bounce. The various examples of anisotropy growth in Bianchi-I model universe shows the complex nature of the problem at hand.