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.
