Gravity from the determinant of the energy-momentum: Astrophysical implications

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 = |det.T|/|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 similar to -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 the gravity-matter coupling can lead to a rich phenomenology in gravitational physics. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.

Automated summary

This paper explores the application of determinants of second-rank tensors in forming generally invariant terms, especially in the volume element of gravitational actions. The authors extend the action of matter fields by introducing an arbitrary function f(D) of the determinants of their energy-momentum and the metric. They derive the gravitational field equations and examine the nonlinear terms induced by the determinant, specifically the inverse of the energy-momentum tensor. The paper also discusses the implications of these extensions and proposes a scale-free model for the gravitational-matter coupling.