Applications of Cosmological Perturbation Theory in the Late Universe

Abstract

In this thesis, we discuss some of the applications of cosmological perturbation theory in the late universe. We begin by reviewing the tools used to understand the standard model of cosmology theoretically and to compute its observational consequences, including a detailed exposition of cosmological perturbation theory. We then describe the results in this thesis; we present novel analytical solutions for linear-order gravitational waves or tensor perturbations in a flat Friedmann-Robertson-Walker universe containing two perfect fluids -- radiation and pressureless dust -- and allowing for neutrino anisotropic stress. One of the results applies to any sub-horizon gravitational wave in such a universe. Another result applies to gravitational waves of primordial origin (for example, produced during inflation) and works both before and after they cross the horizon. These results improve on analytical approximations previously set out in the literature. Comparison with numerical solutions shows that both these approximations are accurate to within 1% or better, for a wide range of wave-numbers relevant for cosmology. We present a new and independent approach to computing the relativistic galaxy number counts to second order in cosmological perturbation theory. We also derive analytical expressions for the full second-order relativistic observed redshift, for the angular diameter distance and the volume spanned by a survey. We then compare our result with previous works which compute the general distance-redshift relation, finding that our result is in agreement at linear and leading nonlinear order. Lastly, we briefly study a class of almost scale-invariant Gauss-Bonnet modified gravity theory and derive the Einstein-like field equations to first order in cosmological perturbation theory in longitudinal gauge.

arXiv comment149 pages, 11 figures, Doctoral Thesis. arXiv admin note: text overlap with arXiv:1911.08313 by other authors

References in corpus (51)

• The Cosmological Constant and Dark Energy
• Modified Gravity and Cosmology
• The Cosmological Constant
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• Modified Gauss-Bonnet theory as gravitational alternative for dark energy
• A Cosmology Calculator for the World Wide Web
• Covariant Galileon
• Dark energy in modified Gauss-Bonnet gravity: late-time acceleration and the hierarchy problem
• Gauss-Bonnet dark energy
• Cosmological perturbations
• Are f(R) dark energy models cosmologically viable ?
• The linear power spectrum of observed source number counts
• What galaxy surveys really measure
• Modified gravity and its reconstruction from the universe expansion history
• Fundamental Physics with the Square Kilometre Array
• Cosmological reconstruction of realistic modified F(R) gravities
• Lecture Notes on General Relativity
• New Perspective on Galaxy Clustering as a Cosmological Probe: General Relativistic Effects
• Damping of Tensor Modes in Cosmology
• Large-scale clustering of galaxies in general relativity
• Charged Black Holes in AdS Spaces in $4D$ Einstein Gauss-Bonnet Gravity
• General Relativistic Description of the Observed Galaxy Power Spectrum: Do We Understand What We Measure?
• Tensor Perturbations in Inflationary Models as a Probe of Cosmology
• xPert: Computer algebra for metric perturbation theory
• Cosmic Microwave Background Fluctuations from Gravitational Waves: An Analytic Approach
• Ghost instabilities of cosmological models with vector fields nonminimally coupled to the curvature
• Stability of the Einstein static universe in f(R) gravity
• Third order equations of motion and the Ostrogradsky instability
• (Mis-)Interpreting supernovae observations in a lumpy universe
• Beyond the Linear-Order Relativistic Effect in Galaxy Clustering: Second-Order Gauge-Invariant Formalism
• Cosmic Rulers
• Galaxy number counts to second order and their bispectrum
• The extended Baryon Oscillation Spectroscopic Survey (eBOSS): a cosmological forecast
• Ghost-free Gauss-Bonnet Theories of Gravity
• The bispectrum of relativistic galaxy number counts
• Kinetic vs. Thermal-Field-Theory Approach to Cosmological Perturbations
• Testing Modified Gravity with Wide Binaries in GAIA DR2
• CBR anisotropy from primordial gravitational waves in inflationary cosmologies
• The luminosity distance-redshift relation up to second order in the Poisson gauge with anisotropic stress
• A Concise Introduction to Perturbation Theory in Cosmology
• An analytic description of the damping of gravitational waves by free streaming neutrinos
• Testing Modified Gravity Theories via Wide Binaries and GAIA
• Unified Treatment of the Luminosity Distance in Cosmology
• Euclid space mission: a cosmological challenge for the next 15 years
• Vector and tensor contributions to the curvature perturbation at second order
• Cosmological Evolution of Scale-invariant Gravity Waves
• Fluctuations of differential number counts of radio continuum sources
• Coupled Evolution of Primordial Gravity Waves and Relic Neutrinos
• Simple Analytical Methods for Computing the Gravity-Wave Contribution to the Cosmic Background Radiation Anisotropy
• Non-linear effects in early Universe cosmology
• Double power series method for approximating cosmological perturbations