Determinant-Gravity: Cosmological implications

Abstract

We analyze the action $\int d^{4}x\sqrt{\det ||\mathcal{B}{g}_{\mu \nu }+\mathcal{C}{R}_{\mu \nu }}||$ 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 $1/m^2$, 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.

revtex format, 5 pages,8 figures,references added