Pseudo Z-symmetric spacetimes with harmonic conformal curvature tensor in F(R)-gravity

Abstract

The present paper is concerned with the study of pseudo Z-symmetric spacetimes (in short, (PZS)4) admitting harmonic conformal curvature tensor in F(R)-gravity. First, we prove that a (PZS)4 spacetime admitting harmonic conformal curvature tensor is conformally flat and this spacetime is a RW spacetime. For these manifolds, we determine the scale factor a(t) in a spatially flat RW spacetime and we obtain the scalar curvature of this spacetime. We find the properties of (PZS)4 spacetimes with harmonic conformal curvature tensor. After that, the isotropic pressure and the energy density are found for such a manifold in F(R)-gravity. At the end, choosing F(R)=R, we prove that the density parameter is 1 and this spacetime has the properties of type I (Big Rip).