Ricci-Determinant Gravity: Dynamical Aspects and Astrophysical Implications

TL;DR

This paper introduces Ricci-determinant gravity, a modified theory of gravity involving the determinant of the Ricci tensor, analyzing its effects on relativistic stars and potential cosmological implications.

Contribution

It proposes a novel gravity model based on the Ricci determinant, derives equations for stellar structures, and identifies bounds where deviations from general relativity become significant.

Findings

Upper bound on Eddington parameter for neutron star deviations

Disformal metric relates affine connection to fluid energy density and pressure

Significant effects on relativistic star structure and potential cosmological impact

Abstract

The Palatini gravitational action is enlarged by an arbitrary function $f(X)$ of the determinants of the Ricci tensor and the metric, $X=|\textbf{det}.R|/|\textbf{det}.g|$. The resulting Ricci-determinant theory exhibits novel deviations from general relativity. We study a particular realization where the extension is characterized by the square-root of the Ricci-determinant, $f(X)=\lambda_\text{Edd}\sqrt{X}$, which corresponds to the famous Eddington action. We analyze the obtained equations for a perfect fluid source and show that the affine connection can be solved in terms of the energy density and pressure of the fluid through an obtained disformal metric. As an application, we derive the hydrostatic equilibrium equations for relativistic stars and inspect the significant effects induced by the square-root of the Ricci tensor. We find that an upper bound on $\lambda_{\rm Edd}$, at which deviations from the predictions of general relativity on neutron stars become prominent, corresponds to the hierarchy between the Planck and the vacuum mass scales. The Ricci-determinant gravity that we propose here is expected to have interesting implications in other cosmological domains.