A generalization of unimodular gravity with vacuum-matter energy exchange

TL;DR

This paper proposes a generalized effective gravity theory involving metric determinants, leading to unique cosmological solutions with vacuum-matter energy exchange, where Minkowski spacetime acts as an attractor, and energy-momentum conservation is violated in dynamic backgrounds.

Contribution

It introduces a novel generalization of unimodular gravity incorporating vacuum-matter energy exchange, with implications for cosmological solutions and conservation laws.

Findings

Minkowski spacetime emerges as an attractor in the model.

Energy exchange causes nonstatic cosmological solutions.

Violations of energy-momentum conservation occur in dynamic backgrounds.

Abstract

An effective theory of gravity in the infrared is proposed, which involves the determinant of the metric relative to the determinant of a prior metric taken to be that of Minkowski spacetime. This effective theory can be interpreted as a generalization of unimodular gravity. In a cosmological context with ultrarelativistic or cold matter, the resulting field equations have only one solution, empty Minkowski spacetime (selected by the prior metric of the theory). The introduction of energy exchange between vacuum and matter gives rise to nonstatic cosmic solutions. It is found that Minkowski spacetime (from the prior metric) appears as an attractor of the dynamic equations. A further result is that energy-momentum conservation of any localized material system is violated in a nonconstant gravitational background. The impact for experiment appears, however, negligible if the vacuum-energy mass scale is of order meV.