Determinantal invariant gravity
Einstein-Hilbert action with a determinantal invariant has been considered. The obtained field equation contains the \texttt{inverse Ricci tensor}, $\Re_{αβ}$. 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 $σ$. $σ=0$ gives a trivial solution for constant curvature, $R_{0}$.