Gauge Invariant Cosmological Perturbation Theory

TL;DR

This work develops gauge-invariant cosmological perturbation theory and applies it to texture seeds as a mechanism for large-scale structure formation. It derives the first-order Einstein and conservation equations, extends them to collisionless matter and Boltzmann transport, and analyzes photon propagation including Sachs-Wolfe and light-deflection effects. The study then detailly treats textures in both flat and expanding spaces, computing the induced perturbations in dark matter, baryons, and photons, and predicting CMB signatures that are compared with COBE data. The results suggest textures can yield plausible large-scale structure and CMB patterns, potentially requiring early reionization and benefiting from 3D simulations for robust conclusions.

Abstract

After an introduction to the problem of cosmological structure formation, we develop gauge invariant cosmological perturbation theory. We derive the first order perturbation equations of Einstein's equations and energy momentum ``conservation''. Furthermore, the perturbations of Liouville's equation for collisionless particles and Boltzmann's equation for Compton scattering are worked out. We fully discuss the propagation of photons in a perturbed Friedmann universe, calculating the Sachs--Wolfe effect and light deflection. The perturbation equations are extended to accommodate also perturbations induced by seeds. With these general results we discuss some of the main aspects of the texture model for the formation of large scale structure in the Universe (galaxies, clusters, sheets, voids). In this model, perturbations in the dark matter are induced by texture seeds. The gravitational effects of a spherically symmetric collapsing texture on dark matter, baryonic matter and photons are calculated in first order perturbation theory. We study the characteristic signature of the microwave background fluctuations induced in this scenario and compare it with the COBE observations.