A Concise Introduction to Perturbation Theory in Cosmology

Abstract

We give a concise, self-contained introduction to perturbation theory in cosmology at linear and second order, striking a balance between mathematical rigour and usability. In particular we discuss gauge issues and the active and passive approach to calculating gauge transformations. We also construct gauge-invariant variables, including the second order tensor perturbation on uniform curvature hypersurfaces.

revtex4, 16 pages, 3 figures; v2: minor changes, typos corrected, reference added, version accepted by CQG

References in corpus (14)

• Non-Gaussianity from Inflation: Theory and Observations
• A general proof of the conservation of the curvature perturbation
• Brane-world gravity
• The cosmological gravitational wave background from primordial density perturbations
• Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond
• On the Back Reaction Problem for Gravitational Perturbations
• Coupled dark energy: Towards a general description of the dynamics
• Second-order Perturbations of the Friedmann World Model
• Evolution of second-order cosmological perturbations
• Second-order Gauge Invariant Cosmological Perturbation Theory: -- Einstein equations in terms of gauge invariant variables --
• Conserved non-linear quantities in cosmology
• Adiabatic and entropy perturbations with interacting fluids and fields
• Non-Linear N-Parameter Spacetime Perturbations: Gauge Transformations
• Gauge invariant Boltzmann equation and the fluid limit

Cited by in corpus (35)

• Teleparallel Gravity: From Theory to Cosmology
• The non-adiabatic pressure in general scalar field systems
• The radiative transfer at second order: a full treatment of the Boltzmann equation with polarization
• The intrinsic bispectrum of the Cosmic Microwave Background [PhD thesis]
• Vorticity generation at second order in cosmological perturbation theory
• Calculating Non-adiabatic Pressure Perturbations during Multi-field Inflation
• Second order solutions of cosmological perturbation in the matter dominated era
• Cosmological matching conditions for gravitational waves at second order
• The cosmological backreaction: gauge (in)dependence, observers and scalars
• Estimating the amount of vorticity generated by cosmological perturbations in the early universe
• Three-form inflation and non-Gaussianity
• Viable Gauge Choices in Cosmologies with Non-Linear Structures
• Vector and tensor contributions to the curvature perturbation at second order
• Modelling non-dust fluids in cosmology
• Second Order Perturbations During Inflation Beyond Slow-roll
• The Poisson equation at second order in relativistic cosmology
• Practical tools for third order cosmological perturbations
• Gauge conditions in combined dark energy and dark matter systems
• An Introduction into the Theory of Cosmological Structure Formation
• Evolution of magnetic fields through cosmological perturbation theory
• Comments on gauge-invariance in cosmology
• Cosmological Perturbations: Vorticity, Isocurvature and Magnetic Fields
• BRST Quantization of Cosmological Perturbations
• Post-linear metric of a compact source of matter
• A note on second-order perturbations of non-canonical scalar fields
• Contributions from primordial non-Gaussianity and General Relativity to the galaxy power spectrum
• EBWeyl: a Code to Invariantly Characterize Numerical Spacetimes
• Recombination era magnetic fields from axion dark matter
• Observable predictions of generalised inflationary scenarios
• The Quantum Origin of Cosmic Structure
• Non-linear effects in early Universe cosmology
• A (semi)-exact Hamiltonian for the curvature perturbation $\zeta$
• Gravitational Entropy in Szekeres Class I Models
• Closed Form Solutions To Bosonic Perturbations In General Relativity
• Applications of Cosmological Perturbation Theory in the Late Universe