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 ${\cal B}(R)= \sqrt {R}$ we can restore the Einstein gravity and, if ${\cal B}=m^2$, we obtain the cosmological constant term. Taking ${\cal B} = m^2 + {\cal B}_1 R$ and expanding the action in $1/m^2$, 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 ${\cal B}$ and ${\cal C}$ new cosmological solutions for the Robertson-Walker metric are obtained.