To conserve, or not to conserve: A review of nonconservative theories of gravity

TL;DR

This paper reviews extended theories of gravity that allow for non-conservation of the energy-momentum tensor, exploring their theoretical foundations and implications for dark matter and dark energy phenomenology.

Contribution

It provides a comprehensive review of nonconservative gravity theories, highlighting their theoretical structures and differences from standard conservative models.

Findings

Many extended gravity theories permit non-conservation of energy-momentum.

Some theories incorporate additional constraints to enforce conservation.

Non-conservative theories may better explain dark matter and dark energy phenomena.

Abstract

Apart from the familiar structure firmly-rooted in the general relativistic field equations where the energy--momentum tensor has a null divergence i.e., it conserves, there exists a considerable number of extended theories of gravity allowing departures from the usual conservative framework. Many of these theories became popular in the last few years, aiming to describe the phenomenology behind dark matter and dark energy. However, within these scenarios, it is common to see attempts to preserve the conservative property of the energy--momentum tensor. Most of the time, it is done by means of some additional constraint that ensures the validity of the standard conservation law, as long as this option is available in the theory. However, if no such extra constraint is available, the theory will inevitably carry a non-trivial conservation law as part of its structure. In this work, we review some of such proposals discussing the theoretical construction leading to the non-conservation of the energy--momentum tensor.