A spherically symmetric and stationary universe from a weak modification of general relativity

TL;DR

This paper proposes a weak modification to general relativity that results in a spherically symmetric, stationary universe model, potentially explaining dark energy through an additional polarization mode in linearized gravity.

Contribution

It introduces a new polarization mode in linearized gravity that leads to a stationary universe model and offers insights into dark energy and the Einstein-Vlasov system.

Findings

A third polarization mode exists in the modified gravity theory.

The model suggests a possible identification of dark energy as curvature energy.

The approach provides a new perspective on the Einstein-Vlasov system.

Abstract

It is shown that a weak modification of general relativity, in the linearized approach, renders a spherically symmetric and stationary model of the universe. This is due to the presence of a third mode of polarization in the linearized gravity in which a "curvature" energy term is present. Such an energy can, in principle, be identified as the Dark Energy. The model can also help to a better understanding of the framework of the Einstein-Vlasov system.