Gravity from the Determinant of the Energy-Momentum: Astrophysical Implications

TL;DR

This paper introduces a novel gravity model based on the determinant of the energy-momentum tensor, deriving new field equations, and explores its astrophysical implications, especially for neutron stars, while maintaining consistency with early universe nucleosynthesis.

Contribution

It extends gravitational action by a function of the energy-momentum determinant, deriving new field equations, and analyzing astrophysical effects, notably on neutron star structure.

Findings

Differences in neutron star mass-radius relations for specific parameter values.

The model does not alter primordial nucleosynthesis predictions.

Proposes a scale-free gravity-matter coupling with rich phenomenology.

Abstract

Determinants of the second-rank tensors stand useful in forming generally invariant terms as in the case of the volume element of the gravitational actions. Here, we extend the action of the matter fields by an arbitrary function $f(D)$ of the determinants of their energy-momentum, and the metric, $D=|\textbf{det}.T|/|\textbf{det}.g|$. We derive the gravitational field equations and examine the nonlinear terms induced by the determinant, specifically, the inverse of the energy-momentum tensor. We also show that these extensions require a nonzero stress-energy tensor for the vacuum. We propose a scale-free model, $f(D)=\lambda D^{1/4}$, and show how it induces the familiar invariant terms formed by the trace of the energy-momentum tensor by expanding the action around the stress-energy of the vacuum. We study the hydrostatic equilibrium equations for a neutron star by providing relevant values of the dimensionless constant $\lambda$. We show that the differences from the predictions of general relativity, in the mass-radius relations, which are sensitive to the equations of state, are conspicuous for $\lambda \sim -10^{-2}$. We also show that the model does not affect the predictions on the primordial nucleosynthesis when it is applied to the early radiation era. This novel and unfamiliar type of gravity-matter coupling can lead to a rich phenomenology in gravitational physics.