Local spherically symmetric perturbations of spatially flat Friedmann models

TL;DR

This paper analyzes linear spherically symmetric perturbations in flat Friedmann models, focusing on their smooth joining at the sound horizon and their physical interpretation as matter redistribution.

Contribution

It provides a solution to Einstein's equations for local perturbations in flat Friedmann models with a linear equation of state, emphasizing the junction at the sound horizon.

Findings

Perturbations are smoothly joined at the sound horizon.

Solutions are obtained in linear approximation near the sound horizon.

Perturbations can be interpreted as matter redistribution events.

Abstract

The spherically symmetric perturbations in the spatially flat Friedman models are considered. It is assumed that the Friedmannian density and pressure are related through a linear equation of state. The perturbation is joined smoothly with an unperturbed Friedmann's background at the sound horizon of perturbation. Such junction is in accordance with the "birth" of a local perturbation as a result of the redistribution of matter. The solution of the Einstein's equations is obtained in linear approximation on a Friedmann's background near the the sound horizon of perturbation.