Conservation Laws and Cosmological Perturbations in Curved Universes

TL;DR

This paper generalizes conservation laws used for setting initial conditions in cosmological perturbations to include curved universes, providing a geometric interpretation and extending their applicability beyond flat models.

Contribution

It extends pseudo-tensor conservation laws from flat to curved Friedmann-Lemaître universes, offering a unified framework for initial conditions in various cosmological geometries.

Findings

Generalized conservation laws to all curvature parameters (K≠0)

Provided a geometric interpretation of the conservation laws

Enabled consistent initial condition setting for curved universes

Abstract

When working in synchronous gauges, pseudo-tensor conservation laws are often used to set the initial conditions for cosmological scalar perturbations, when those are generated by topological defects which suddenly appear in an up to then perfectly homogeneous and isotropic universe. However those conservation laws are restricted to spatially flat (K=0) Friedmann-Lema\^\i tre spacetimes. In this paper, we first show that in fact they implement a matching condition between the pre- and post- transition eras and, in doing so, we are able to generalize them and set the initial conditions for all $K$. Finally, in the long wavelength limit, we encode them into a vector conservation law having a well-defined geometrical meaning.