Determinant-Gravity: Cosmological implications

We analyze the action $\int d^4x \sqrt{\det||{\cal B} g_{\mu\nu}+ {\cal C} R_{\mu\nu}}||$ as a possible alternative or addition to the Einstein gravity. Choosing a particular form of $\mathcal{B}(R)=\sqrt{R}$ we can restore the Einstein gravity and, if $\mathcal{B}=m^2$, we obtain the cosmological constant term. Taking $\mathcal{B}=m^2+{\mathcal{B}}_{1}R$ and expanding the action in $1\mathrm{/}{m}^2$, we obtain as a leading term the Einstein Lagrangian with a cosmological constant proportional to $m^4$ and a series of higher order operators. In general case of non-vanishing $\mathcal{B}$ and $\mathcal{C}$ new cosmological solutions for the Robertson-Walker metric are obtained.