The Layzer-Irvine equation in theories with non-minimal coupling between matter and curvature

TL;DR

This paper derives the Layzer-Irvine equation within alternative gravity theories featuring non-minimal matter-curvature coupling, and applies it to analyze galaxy cluster Abell 586.

Contribution

It introduces a generalized Layzer-Irvine equation for non-minimal coupling theories and demonstrates its application to real galaxy cluster data.

Findings

Derived the Layzer-Irvine equation for non-minimal coupling theories

Applied the equation to galaxy cluster Abell 586

Provided insights into matter density profiles in alternative gravity

Abstract

We derive the Layzer-Irvine equation for alternative gravitational theories with non-minimal coupling between curvature and matter for an homogeneous and isotropic Universe. As an application, we study the case of Abell 586, a relaxed and spherically symmetric galaxy cluster, assuming some matter density profiles.