Non-vacuum plane symmetric universe in f (R) gravity

In this paper, we investigate a non-static plane symmetric model in the presence of perfect fluid distribution in f(R) theory of gravity. Here R is the Ricci scalar of the space-time. We have derived, explicitly, the field equations of this theory. We have obtained a determinate solution of the field equations using (i) the shear scalar sigma of the space-time is proportional to expansion scalar which leads to a relation between metric potentials, and (ii) a power law between the scalaron function F of the theory and average scale factor a (t) of the universe. The solution obtained represents an implicit exponential model of the universe with a variable deceleration parameter. This is a unique feature of our model which is different from other models obtained assuming time varying deceleration parameter. We have found the cosmological parameters, namely, pressure, energy density, spatial volume, mean Hubble's parameter, shear, average anisotropy and expansion scalars of our model which are significant in the discussion of cosmology. We have discussed their physical significance through graphical representation. It is observed that the deceleration parameter exhibits a smooth transition from early deceleration to late time acceleration of the universe. It is also observed that our model satisfies the null energy condition.