Pre-Galaxy Formation: A Non-Linear Analysis of the Evolution of Cosmological Perturbations

TL;DR

This paper presents a higher-order, analytical study of cosmological perturbations in a Friedman universe using the PMF method, revealing faster growth of instabilities and boundary conditions for their development.

Contribution

It introduces a simplified gauge-based method for higher-order perturbation analysis and provides analytical solutions up to third order for a dust universe.

Findings

Instable perturbations grow faster than first-order predictions.

Large-scale perturbations grow moderately, indicating a boundary for instability.

Supports the conjecture of rapid growth of instabilities in cosmological perturbations.

Abstract

A higher-order analysis of the evolution of cosmological perturbations in a Friedman universe is given by using the PMF method. The essence of the PMF approach is to choose a gauge where all fluctuations of the density, the pressure, and the four-velocity vanish. In that gauge, even in higher orders, the perturbation field equations simplify considerably; they can be decoupled and - for simple equations of state - also be solved analytically. We give the solution for the dust universe up to third order. Comparison of these solutions strongly supports the conjecture that in general instable perturbations grow much faster than they do according to the first-order analysis. However, perturbations with very large spatial extension behave differently; they grow only moderatly. Thus, an upper boundary of the region of instability seems to exist.