Determinantal invariant gravity

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, $R_{0}$.