Exact solutions of Bianchi-type I and V spacetimes in the f(R) theory of gravity

In this paper, the crucial phenomenon of the expansion of the universe has been discussed. For this purpose, we study the vacuum solutions of Bianchi-type I and V spacetimes in the framework of f (R) gravity. In particular, we find two exact solutions in each case using the variation law of Hubble parameter. These solutions correspond to two models of the universe. The first solution gives a singular model, while the second solution provides a non-singular model. The physical behavior of these models is discussed. Moreover, the function of the Ricci scalar is evaluated for both models in each case.