Cosmological perturbation theory

Abstract

This is a review on cosmological perturbation theory. After an introduction, it presents the problem of gauge transformation. Gauge invariant variables are introduced and the Einstein and conservation equations are written in terms of these variables. Some examples, especially perfect fluids and scalar fields are presented in detail. The generation of perturbations during inflation is studied. Lightlike geodesics and their relevance for CMB anisotropies are briefly discussed. Perturbation theory in braneworlds is also introduced.

my course at the Second Aegean Summerschool on the Early Universe, 39 pages (I have corrected some typos)

References in corpus (4)

• Cosmic Structure Formation with Topological Defects
• Cosmological perturbations in the bulk and on the brane
• Slowly decaying tails of massive scalar fields in spherically symmetric spacetimes
• Reproducing Cosmic Microwave Background anisotropies with mixed isocurvature perturbations

Cited by in corpus (27)

• Occurrence of exact $R^2$ inflation in non-local UV-complete gravity
• Gauge-Invariant Perturbations in Hybrid Quantum Cosmology
• Cosmological perturbations in Hybrid Loop Quantum Cosmology: Mukhanov-Sasaki variables
• The isocurvature fraction after WMAP 3-year data
• Circuit Complexity From Cosmological Islands
• Observational signatures of modified gravity on ultra-large scales
• Review on stochastic approach to inflation
• Cosmological perturbations in an effective and genuinely phantom dark energy Universe
• Gauges and Cosmological Backreaction
• Averaging Robertson-Walker Cosmologies
• Cosmology with a light ghost
• Braneworlds
• Gauge invariant canonical cosmological perturbation theory with geometrical clocks in extended phase space - a review and applications
• An analytic approach to baryon acoustic oscillations
• Backreaction: Gauge and Frame Dependences
• On the perturbation theory in spatially closed background
• Evolution of magnetic fields through cosmological perturbation theory
• Scalar induced gravitational waves review
• Noncommutative fluid and Growing Modes of Inhomogeneity in (Newtonian) Cosmology
• Testing quantum gravity with primordial gravitational waves
• Evolution of the spectral index after inflation
• Cosmological Geometric Phase From Pure Quantum States: A study without/with having Bell's inequality violation
• Scale-free power spectrums in the delayed cosmology
• Inflation and Primordial Perturbations in Fractal Cosmology
• Perturbation Theory in the Minimally Extended Varying Speed of Light (meVSL) Model
• Second Order perturbation Theory: A covariant approach involving a barotropic equation of state
• A note on the (non-)conservation of curvature perturbation