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

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).