An example of rotating cosmological universe in modified gravity

This research study is primarily focus on investigating an exact vacuum solution characterized by a negative cosmological constant, Lambda<0, within the framework of a modified gravity theory. Our specific focus is on a novel theory known as Ricci-inverse gravity. This vacuum solution is representative of an Anti-de Sitter (AdS) space, which, in general relativity, serves as a space-time exhibiting properties akin to a time-machine. Significantly, we demonstrate that this AdS space-time is a valid solution within the Ricci-inverse gravity theory as well. This outcome implies that Ricci-inverse gravity also allows the formation of closed time-like curves, analogous to what is observed in the context of general relativity. The investigation into Ricci-inverse gravity involves introducing the function f(R, A) into the Lagrangian of the system. We consider three distinct scenarios to explore the implications of different choices for the function. The first scenario involves selecting f(R,A)=(R+kappa A), the second one adopts f(R,A)=(R+gamma A(mu nu) A(mu nu)), and the third scenario employs the function f(R,A) = (R+beta R-2)+(kappa A+gamma A(mu nu)A(mu nu)), where kappa,beta and gamma serve as the coupling constants. In each of these scenarios, we derive the modified field equations and subsequently solve them under the assumption of vacuum as the matter-energy content. Notably, our results demonstrate that the cosmological constant Lambda undergoes modification based on the coupling constants in each case. Thus, in Ricci-inverse gravity, we establish that this modified Anti-de Sitter (AdS) space-time also serves as a model for a time-machine.