Acceleration of the universe in the Einstein frame of a metric-affine f ( R ) gravity

We show that inflation and current cosmic acceleration can be generated by a metric-affine f(R) gravity formulated in the Einstein conformal frame, if the gravitational Lagrangian L(R) contains both positive and negative powers of the curvature scalar R. In this frame, we give the equations for the expansion of the homogeneous and isotropic matter-dominated universe in the case L(R)=R+{R^3}/{β^2}-{α^2}/{3R}, where αand βare constants. We also show that gravitational effects of matter in such a universe at very late stages of its expansion are weakened by a factor that tends to 3/4, and the energy density of matter εscales the same way as in the Λ-CDM model only when κ*ε<