Determinantal invariant gravity

TL;DR

This paper explores a modified gravity theory incorporating a determinantal invariant in the Einstein-Hilbert action, leading to field equations involving the inverse Ricci tensor and revealing new constant curvature solutions depending on a parameter.

Contribution

It introduces a novel determinantal invariant into the gravity action and derives resulting field equations with inverse Ricci tensor, analyzing their solutions.

Findings

Field equations contain inverse Ricci tensor

Constant curvature solutions vary with parameter σ

Trivial solution for σ=0

Abstract

Einstein-Hilbert action with a determinantal invariant has been considered. The obtained field equation contains the \texttt{inverse Ricci tensor}, $\Re_{\alpha\beta}$. The linearized solution of invariant has been examined, and constant curvature space-time metric solution of the field equation gives different curvature constant for each values of $\sigma$. $\sigma=0$ gives a trivial solution for constant curvature, $R_{0}$.