Layzer-Irvine equation: new perspectives and the role of interacting dark energy

TL;DR

This paper generalizes the Layzer-Irvine equation to include interacting dark energy and higher-dimensional objects, providing new tools to study cosmic structures and dark sector interactions.

Contribution

It derives a generalized Layzer-Irvine equation incorporating interacting dark energy and extends it to higher dimensions and cosmic strings, offering novel insights into cosmic dynamics.

Findings

Derived the Layzer-Irvine equation with arbitrary dark energy equation of state.

Extended the equation to higher-dimensional universes and p-branes.

Generalized the equation to include non-minimal dark matter-dark energy interactions.

Abstract

We derive the Layzer-Irvine equation in the presence of a homogeneous (or quasi-homogeneous) dark energy component with an arbitrary equation of state. We extend the Layzer-Irvine equation to homogeneous and isotropic universes with an arbitrary number of dimensions and obtain the corresponding virial relation for sufficiently relaxed objects. We find analogous equations describing the dynamics of cosmic string loops and other p-branes of arbitrary dimensionality, discussing the corresponding relativistic and non-relativistic limits. Finally, we generalize the Layzer-Irvine equation to account for a non-minimal interaction between dark matter and dark energy, discussing its practical use as a signature of such an interaction.