Integral Constraints On cosmological Perturbations and their Energy

TL;DR

This paper explores the connection between integral equations and the energy and center of mass of matter perturbations in cosmology, deriving constraints for localized perturbations and illustrating with an example.

Contribution

It establishes a link between Traschen's integral equations and the energy and center of mass of matter perturbations in cosmological spacetimes, providing new integral constraints.

Findings

Derived integral constraints for localized perturbations.

Connected integral equations with physical quantities like energy and center of mass.

Illustrated the theoretical results with a simple example.

Abstract

We show the relation between Traschen's integral equations and the energy, and ``position of the centre of mass'', of the matter perturbations in a Robertson-Walker spacetime. When the perturbations are ``localised'' we get a set of integral constraints that includes hers. We illustrate them on a simple example.