Exact vacuum solutions to modified Einstein field equations in f (R) gravity

Considering the plane symmetric non-static spacetimes in the context of f(R) gravity, we obtain exact solutions of the vacuum field equations by assuming constant scalar curvature. By suitable transformations, it is shown that the obtained solutions can be transformed to Bianchi type V, a type of Taub's and the De Sitter solutions. Of particular interest is a solution that represents a model that has initial singularity and under an appropriate transformation can be converted to a Bianchi-type V model. This solution, like the Bianchi type V model, leads to predictions about evolution in the sense of an expanding universe starting from an initial singularity. In this context, we show that the expansion of the universe in f(R) gravity can be explained without invoking the cosmological constant .