Cosmological dynamics of magnetic Bianchi I in viable f(R) models of gravity

Standard dynamical system analysis of Einstein-Maxwell equation in f(R) theories is considered in this work. We investigate cosmological dynamics of a uniform magnetic field in the Orthogonal Spatially Homogeneous (OSH) Bianchi I universe with viable f(R) models of gravity. In this work, the f(R)=R−αRn and f(R)=Rb−Λc models are examined by using our dynamical system analysis. Our results show that both of two f(R) models have a viable cosmological consequence identical to the analysis present in Amendola and Tsujikawa (2008) for the FLRW background. Contrary to Amendola and Tsujikawa (2008), we discover in our models that there is an additional anisotropic and non-zero cosmological magnetic fields fixed point emerging before the present of the standard matter epoch. This means that the universe has initially isotropic stage with the intermediated epoch as the anisotropic background and it ends up with the isotropic late-time acceleration. The primordial magnetic fields play a crucial role of the shear evolutions obtained from these two models which have the same scaling of the cosmic time as σ∼t−13, instead of σ∼t−1 for the absence of the primordial magnetic cases.