CMB Anisotropies at Second-Order II: Analytical Approach

Abstract

We provide an analytical approach to the second-order Cosmic Microwave Background (CMB) anisotropies generated by the non-linear dynamics taking place at last scattering. We study the acoustic oscillations of the photon-baryon fluid in the tight coupling limit and we extend at second-order the Meszaros effect. We allow for a generic set of initial conditions due to primordial non-Gaussianity and we compute all the additional contributions arising at recombination. Our results are useful to provide the full second-order radiation transfer function at all scales necessary for establishing the level of non-Gaussianity in the CMB.

38 pages, LaTeX file; typos corrected, discussion improved in Sec. IIIA and VII, matching the version published in JCAP

References in corpus (2)

• CMB Anisotropies at Second Order I
• Generating the Curvature Perturbation at the End of Inflation in String Theory

Cited by in corpus (85)

• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Relativistic cosmology and large-scale structure
• Hunting for Primordial Non-Gaussianity in the Cosmic Microwave Background
• CMB at 2x2 order: the dissipation of primordial acoustic waves and the observable part of the associated energy release
• The Initial Spin Probability Distribution of Primordial Black Holes
• Detectability of the effect of Inflationary non-Gaussianity on halo bias
• Anisotropies and non-Gaussianity of the Cosmological Gravitational Wave Background
• Probing Anisotropies of the Stochastic Gravitational Wave Background with LISA
• The bispectrum of redshifted 21-cm fluctuations from the dark ages
• Characterizing the Cosmological Gravitational Wave Background Anisotropies and non-Gaussianity
• From Primordial Black Holes Abundance to Primordial Curvature Power Spectrum (and back)
• Large Nongaussianity from Nonlocal Inflation
• The cosmic microwave background bispectrum from the non-linear evolution of the cosmological perturbations
• Primordial Non-Gaussianity in the Cosmic Microwave Background
• The radiative transfer at second order: a full treatment of the Boltzmann equation with polarization
• CMB lensing and primordial non-Gaussianity
• Non-Gaussianity and the Cosmic Microwave Background Anisotropies
• Mixing of blackbodies: entropy production and dissipation of sound waves in the early Universe
• The CMB bispectrum in the squeezed limit
• The Imprint of Relativistic Particles on the Anisotropies of the Stochastic Gravitational-Wave Background
• Sachs-Wolfe at second order: the CMB bispectrum on large angular scales
• Cosmological Perturbations at Second Order and Recombination Perturbed
• Cosmic microwave background bispectrum on small angular scales
• The intrinsic bispectrum of the Cosmic Microwave Background [PhD thesis]
• Isocurvature, non-gaussianity and the curvaton model
• The impact of cosmic neutrinos on the gravitational-wave background
• CMB anisotropies at second order III: bispectrum from products of the first-order perturbations
• Predictions for Nongaussianity from Nonlocal Inflation
• Non-Gaussianity in the Cosmic Microwave Background Anisotropies at Recombination in the Squeezed limit
• The CMB bispectrum from recombination
• Matter bispectrum in cubic Galileon cosmologies
• Crinkles in the last scattering surface: Non-Gaussianity from inhomogeneous recombination
• Signatures of Horndeski gravity on the Dark Matter Bispectrum
• Inflationary trispectrum from graviton exchange
• Analytic formulae of the CMB bispectra generated from non-Gaussianity in the tensor and vector perturbations
• Cross-correlating Astrophysical and Cosmological Gravitational Wave Backgrounds with the Cosmic Microwave Background
• Boltzmann hierarchy for the cosmic microwave background at second order including photon polarization
• Non-Gaussianities from Perturbing Recombination
• Relativistic wide-angle galaxy bispectrum on the light-cone
• Signatures of Primordial non-Gaussianities in the Matter Power-Spectrum and Bispectrum: the Time-RG Approach
• Primordial B-mode Diagnostics and Self Calibrating the CMB Polarization
• Cosmological perturbation theory and quantum gravity
• Bispectrum of cosmological density perturbations in the most general second-order scalar-tensor theory
• Contributions to the Dark Matter 3-Pt Function from the Radiation Era
• Impact of anisotropic stress of free-streaming particles on gravitational waves induced by cosmological density perturbations
• Feeding your Inflaton: Non-Gaussian Signatures of Interaction Structure
• On the non-Gaussianity from Recombination
• Gauge invariant Boltzmann equation and the fluid limit
• The intrinsic B-mode polarisation of the Cosmic Microwave Background
• Cosmic Microwave Background Acoustic Peak Locations
• Weak lensing induced by second-order vector mode
• The Intrinsic Matter Bispectrum in $\Lambda$CDM
• Non-Gaussianities in extended D-term inflation
• Impact of polarisation on the intrinsic CMB bispectrum
• Magnetic field spectrum at cosmological recombination revisited
• The structure of correlation functions in single field inflation
• Impact of Uncertainties in the Cosmological Parameters on the Measurement of Primordial non-Gaussianity
• Interpreting the CMB aberration and Doppler measurements: boost or intrinsic dipole?
• Analytic solutions of scalar perturbations induced by scalar perturbations
• Non-Gaussianity of secondary anisotropies from ACTPol and Planck
• Initial conditions for cold dark matter particles and General Relativity
• More on crinkles in the last scattering surface
• The full CMB temperature bispectrum from single-field inflation
• Newton to Einstein - dust to dust
• Geodesic "curve"-of-sight formulae for the cosmic microwave background: a unified treatment of redshift, time delay, and lensing
• B polarization of cosmic background radiation from second-order scattering sources
• A New Solution for the Observed Isotropic Cosmic Birefringence Angle and its Implications for the Anisotropic Counterpart through a Boltzmann Approach
• A new line-of-sight approach to the non-linear Cosmic Microwave Background
• CMB temperature anisotropies from third order gravitational perturbations
• Non-Gaussian CMB and LSS statistics beyond polyspectra
• Probing small-scale non-Gaussianity from anisotropies in acoustic reheating
• Testing gravity with non-Gaussianity
• Unified approach to secondary effects on the CMB B-mode polarization
• Second-order Gauge-invariant Cosmological Perturbation Theory: Current Status updated in 2019
• Relics of spatial curvature in the primordial non-gaussianity
• On non-linear CMB temperature anisotropy from gravitational perturbations
• The parity-odd Intrinsic Bispectrum
• CMB Polarization by the Asymmetric Template of Scalar Perturbations
• CMB in the river frame and gauge invariance at second order
• CMB anisotropies at all orders: the non-linear Sachs-Wolfe formula
• A Consistency Relation for the CMB B-mode Polarization in the Squeezed Limit
• CMB spectroscopy at third-order in cosmological perturbations
• Test of the Statistical Isotropy of the Universe using Gravitational Waves
• Second Order perturbation Theory: A covariant approach involving a barotropic equation of state