Inhomogeneities in the early universe from the configuration space perspective

Abstract

We develop a new technique of analyzing the dynamics of cosmological perturbations in the linear regime. The gist of our method, described in Chapters 2 and 3, is to solve the corresponding evolution equations in 1 + 1 space-time dimensions with the initial conditions proportional to a spatial delta function. An arbitrary cosmological perturbation can be described as a superposition of the resulting Green's functions. In Chapter 2 we calculate the Green's functions assuming that prior to recombination photons are tightly coupled to baryons by scattering and neglecting neutrino free-streaming. We find that in the conformal Newtonian gauge a primordial perturbation does not affect the space beyond its acoustic horizon and propagates predominantly as a spherical "shock" that is trailed by a region of finite density and metric perturbation. In Chapter 4 we apply these solutions to analyze the anisotropy of the cosmic microwave background (CMB) radiation. In particular, we observe that wavefront singularities in Green's functions cause temperature anti-correlation for two regions that just established an acoustic contact. The experimental signature of this effect is a distinctive dip in the CMB temperature angular correlation function C([theta]) at [theta][is approzimately equal to] 1.2⁰. Variation of the cosmological parameters [Omega], [Omega]bh2, [Omega]c, n predictably affects the location and the shape of the dip and other C([theta]) characteristics. The acoustic oscillations in CMB angular power spectrum C, appear due to oscillations in the Fourier transform of the Green's functions, having finite spatial extent.

The finite extent and monotonicity of Green's functions greatly reduce CPU time required for numerical calculation of perturbation dynamics. The geometrical part of the calculations connecting the early universe inhomogeneities with the CMB anisotropy spectrum C, in momentum space, can also be sped up by averaging the contributions from different momentum modes over rapid oscillations of a geometrical term. In Chapter 5 we describe implementation of these two ideas as a computer program calculating CMB spectrum within the fluid approximation of Chapter 2. In Chapter 3 we extend Green's function techniques to Boltzmann phase space to incorporate diffusion of massless particles. We obtain a solution for adiabatic perturbations in the radiation dominated universe that includes the dynamics of perturbations in the cosmic background of massless neutrinos.