Notes on pseudo symmetric and pseudo Ricci symmetric generalized Robertson–Walker space-times.

We establish two key results regarding pseudo symmetric and pseudo Ricci symmetric space-times. Firstly, we demonstrate that in pseudo symmetric generalized Robertson-Walker space-times either the scalar curvature remains constant or the associated vector field B i is irrotational. Secondly, in pseudo Ricci symmetric generalized Robertson-Walker space-times, we establish that either the scalar curvature is zero or the associated vector field A i is irrotational. We identify the conditions to ensure both B i and A i of these manifolds are acceleration-free and vorticity-free. We provide evidence that a pseudo symmetric and pseudo Ricci symmetric GRW space-time can be described as a perfect fluid. In a pseudo symmetric space-time, the state equation is given by p = 4 - n 2 n - 2 μ , whereas in a pseudo Ricci symmetric space-time, the state equation takes the form p = 3 - n n - 1 μ , where p and μ are the isotropic pressure and the energy density. It is noteworthy that if n = 4 , a pseudo symmetric space-time corresponds to the dust matter era, while a pseudo Ricci symmetric space-time corresponds to the phantom era. [ABSTRACT FROM AUTHOR]