Cosmological Perturbations at Second Order and Recombination Perturbed

Abstract

We derive the full set of second-order equations governing the evolution of cosmological perturbations, including the effects of the first-order electron number density perturbations, δ_e. We provide a detailed analysis of the perturbations to the recombination history of the universe and show that a perturbed version of the Peebles effective 3-level atom is sufficient for obtaining the evolution of δ_e for comoving wavenumbers smaller than 1Mpc^{-1}. We calculate rigorously the perturbations to the Lyαescape probability and show that to a good approximation it is governed by the local baryon velocity divergence. For modes shorter than the photon diffusion scale, we find that δ_e is enhanced during recombination by a factor of roughly 5 relative to other first-order quantities sourcing the CMB anisotropies at second order. Using these results, in a companion paper we calculate the CMB bispectrum generated during recombination.

47 pages, 6 figures

References in corpus (28)

• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Non-Gaussian features of primordial fluctuations in single field inflationary models
• DBI in the Sky
• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• The imprints of primordial non-gaussianities on large-scale structure: scale dependent bias and abundance of virialized objects
• The primordial density perturbation in the curvaton scenario
• Gravitational Wave Spectrum Induced by Primordial Scalar Perturbations
• A New Calculation of the Recombination Epoch
• Ghost Inflation
• Limits on non-Gaussianities from WMAP data
• New Ekpyrotic Cosmology
• Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond
• Non-Gaussianities in models with a varying inflaton decay rate
• Generating Ekpyrotic Curvature Perturbations Before the Big Bang
• The 21cm angular-power spectrum from the dark ages
• Primordial Bispectrum Information from CMB Polarization
• CMB Anisotropies at Second Order I
• Non-Gaussian Density Fluctuations from Entropically Generated Curvature Perturbations in Ekpyrotic Models
• CMB Anisotropies at Second-Order II: Analytical Approach
• Non-Gaussianities from ekpyrotic collapse with multiple fields
• Lines in the Cosmic Microwave Background Spectrum from the Epoch of Cosmological Hydrogen Recombination
• Re-Ionization and its Imprint on the Cosmic Microwave Background
• Tilted Ghost Inflation
• CMB 3-point functions generated by non-linearities at recombination
• Cosmic microwave background bispectrum on small angular scales
• The impact of cosmic neutrinos on the gravitational-wave background
• Linear effects of perturbed recombination

Cited by in corpus (47)

• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Cosmological Non-Linearities as an Effective Fluid
• Non-Gaussianities in Single Field Inflation and their Optimal Limits from the WMAP 5-year Data
• Hunting for Primordial Non-Gaussianity in the Cosmic Microwave Background
• Primordial non-gaussianity from the bispectrum of 21-cm fluctuations in the dark ages
• The cosmic microwave background bispectrum from the non-linear evolution of the cosmological perturbations
• Primordial Non-Gaussianity in the Cosmic Microwave Background
• Non-Gaussianity and the Cosmic Microwave Background Anisotropies
• A new light on 21 cm intensity fluctuations from the dark ages
• The CMB bispectrum in the squeezed limit
• Sachs-Wolfe at second order: the CMB bispectrum on large angular scales
• The intrinsic bispectrum of the Cosmic Microwave Background [PhD thesis]
• Compensated Isocurvature Perturbations and the Cosmic Microwave Background
• CMB anisotropies at second order III: bispectrum from products of the first-order perturbations
• The CMB bispectrum from recombination
• Non-Gaussianity in the Cosmic Microwave Background Anisotropies at Recombination in the Squeezed limit
• The seed magnetic field generated during recombination
• Analytic formulae of the CMB bispectra generated from non-Gaussianity in the tensor and vector perturbations
• Boltzmann hierarchy for the cosmic microwave background at second order including photon polarization
• Consistency of Planck, ACT and SPT constraints on magnetically assisted recombination and forecasts for future experiments
• Cosmology with varying fundamental constants from hyperlight, coupled scalars
• The EFT Likelihood for Large-Scale Structure
• Limits on Second-Order Non-Gaussianity from Minkowski Functionals of WMAP Data
• Impact of anisotropic stress of free-streaming particles on gravitational waves induced by cosmological density perturbations
• Weak lensing induced by second-order vector mode
• The Intrinsic Matter Bispectrum in $\Lambda$CDM
• Impact of polarisation on the intrinsic CMB bispectrum
• Spectral distortion anisotropies from single-field inflation
• Magnetic field spectrum at cosmological recombination revisited
• The full CMB temperature bispectrum from single-field inflation
• Perturbed Recombination from Dark Matter Annihilation
• Geodesic "curve"-of-sight formulae for the cosmic microwave background: a unified treatment of redshift, time delay, and lensing
• Exploring compensated isocurvature perturbations with CMB spectral distortion anisotropies
• Non-Gaussian CMB and LSS statistics beyond polyspectra
• CMB spectral distortions as solutions to the Boltzmann equations
• 21cmFirstCLASS II. Early linear fluctuations of the 21cm signal
• Unified approach to secondary effects on the CMB B-mode polarization
• Second-order Gauge-invariant Cosmological Perturbation Theory: Current Status updated in 2019
• On non-linear CMB temperature anisotropy from gravitational perturbations
• Stability of small-scale baryon perturbations during cosmological recombination
• CMB in the river frame and gauge invariance at second order
• CMB anisotropies at all orders: the non-linear Sachs-Wolfe formula
• Non-linear effects in early Universe cosmology
• Magnetic fields from small-scale primordial perturbations
• O-V-S-Z and friends: Non-Gaussianity from inhomogeneous reionization
• Probing small-scale baryon and dark matter isocurvature perturbations with cosmic microwave background anisotropies
• Leptogenesis with perturbations in type-II and type-III seesaw models