Certain applications of pseudo generalized Z-recurrent spacetimes in modified gravity

In this paper, we introduce and investigate a novel space-time, named a pseudo generalized Z-recurrent spacetime. Next, we illustrate that a pseudo generalized Z-recurrent spacetime with Codazzi type of Ricci tensor is a pseudo quasi-Einstein spacetime under certain condition; whereas the space-time is reduced to a nearly quasi-Einstein spacetime if we consider a parallel Ricci tensor. Moreover, we establish that a pseudo generalized Z-recurrent generalized Robertson–Walker space-time becomes a perfect fluid spacetime. Finally, we examine the effect of such spacetime under [Formula: see text] and [Formula: see text] gravity scenario and we determine the connection between the deceleration, jerk, and snap parameters using the flat Friedmann–Robertson–Walker metric and also with the help of the model [Formula: see text], verify Null, Weak, Dominant and Strong energy condition.