Determinant-Gravity: Cosmological implications

TL;DR

This paper explores a modified gravity action involving determinants of a combination of metric and Ricci tensor, deriving cosmological solutions and connecting to Einstein gravity and cosmological constants.

Contribution

It introduces a novel determinant-based gravity action that generalizes Einstein gravity and yields new cosmological solutions.

Findings

Reproduces Einstein gravity with specific parameter choices.

Derives cosmological constant from the action.

Finds new solutions for Robertson-Walker metric.

Abstract

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.