Analytic approach to the CMB polarizations generated by relic gravitational waves

Abstract

By Polnarev's method we analytically calculate the polarization spectra of the cosmic microwave background radiation (CMB) generated by cosmic relic gravitational waves (RGW). In this analytic approach the physics involved in this generating process is more transparent. Consequently, the effects due to various elements of physics can be isolated easily. In solving the equation for evolution of RGW in the expanding universe, both the sudden transition and the WKB approximation for the scale factor during the radiation-matter transition have been taken. To describe more precisely the decoupling process, we have introduced an analytic expression for the visibility function, consisting of two pieces of half-Gaussian curves. We also include the damping on polarizations due to the photon diffusion up to the second order of the tight coupling. Analytic polarization spectra $C_l^{XX}$ have been obtained with the following several improvements over the previous results. 1. The approximate analytic result is quite close to the numerical one evaluated from the cmbfast code, especially, for the first three peaks of the spectrum that are observable (see the text).

27 pages including 15 figures. Only style is revised

References in corpus (17)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Three Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Polarization Analysis
• Cosmological parameters from combining the Lyman-alpha forest with CMB, galaxy clustering and SN constraints
• The Scientific Programme of Planck
• Cosmic Microwave Background Fluctuations from Gravitational Waves: An Analytic Approach
• DASI Three-Year Cosmic Microwave Background Polarization Results
• Implications of the Cosmic Background Imager Polarization Data
• Considerations in optimizing CMB polarization experiments to constrain inflationary physics
• Upper Limits on a Stochastic Background of Gravitational Waves
• Relic gravitational waves and their detection
• Relic Gravitational Waves in the Accelerating Universe
• Comment on "Damping of Tensor Modes in Cosmology"
• First measurements of the polarization of the cosmic microwave background radiation at small angular scales from CAPMAP
• Task Force on Cosmic Microwave Background Research
• An exact analytic spectrum of relic gravitational waves in an accelerating universe
• Theory of Cosmic Microwave Background Polarization
• CLOVER - A new instrument for measuring the B-mode polarization of the CMB

Cited by in corpus (67)

• Probing polarization states of primordial gravitational waves with CMB anisotropies
• Relic gravitational waves and their detection
• Spectrum of Primordial Gravitational Waves in Modified Gravities: A Short Overview
• Analytic spectrum of relic gravitational waves modified by neutrino free streaming and dark energy
• Stochastic backgrounds of relic gravitons, T$\Lambda$CDM paradigm and the stiff ages
• Relic Gravitational Waves with A Running Spectral Index and Its Constraints at High Frequencies
• Separating E and B types of polarization on an incomplete sky
• Analytic Spectra of CMB Anisotropies and Polarization Generated by Relic Gravitational Waves with Modification due to Neutrino Free-Streaming
• Using polarized maser to detect high-frequency relic gravitational waves
• Detecting relic gravitational waves in the CMB: Optimal parameters and their constraints
• Performance forecasts for the primordial gravitational wave detection pipelines for AliCPT-1
• On the road to discovery of relic gravitational waves: The TE and BB Correlations in the cosmic microwave background radiation
• Approximate Analytic Spectra of Reionized CMB Anisotropies and Polarization generated by Relic Gravitational Waves
• Modifications by QCD transition and $e^{+}{e}^{-}$ annihilation on analytic spectrum of relic gravitational waves in accelerating universe
• Detecting relics of a thermal gravitational wave background in the early Universe
• The refractive index of relic gravitons
• Vacuum and Gravitons of Relic Gravitational Waves, and Regularization of Spectrum and Energy-Momentum Tensor
• Constraints upon the spectral indices of relic gravitational waves by LIGO S5
• Energy Momentum Pseudo-Tensor of Relic Gravitational Wave in Expanding Universe
• Relic gravitational waves: latest revisions and preparations for new data
• Probing large-scale magnetism with the Cosmic Microwave Background
• Comparison of delensing methodologies and assessment of the delensing capabilities of future experiments
• Probing the statistical properties of CMB $B$-mode polarization through Minkowski Functionals
• Impulsive cylindrical gravitational wave: one possible radiative form emitted from cosmic strings and corresponding electromagnetic response
• Detecting relic gravitational waves in the CMB: Comparison of different methods
• Detecting very-high-frequency relic gravitational waves by electromagnetic wave polarizations in a waveguide
• Improved calculation of relic gravitational waves
• Relic gravitational waves in the light of 7-year Wilkinson Microwave Anisotropy Probe data and improved prospects for the Planck mission
• $f(R)$-Gravity Generated Post-inflationary Eras and their Effect on Primordial Gravitational Waves
• New method to constrain the relativistic free-streaming gas in the Universe
• New Primordial-Magnetic-Field Limit from The Latest LIGO S5 data
• Adiabatic regularization of power spectrum and stress tensor of relic gravitational wave without low-frequency distortion
• Detecting Relic Gravitational Waves in the CMB: Comparison of Planck and Ground-based Experiments
• Second-order cosmological perturbations. I. Produced by scalar-scalar coupling in synchronous gauge
• Post-inflationary thermal histories and the refractive index of relic gravitons
• Cosmic backgrounds of relic gravitons and their absolute normalization
• Second-order cosmological perturbations. IV. Produced by scalar-tensor and tensor-tensor couplings during the radiation dominated stage
• Relic Gravitational Waves And CMB Polarization In The Accelerating Universe
• Second-order cosmological perturbations. II. Produced by scalar-tensor and tensor-tensor couplings
• Using pulsar timing arrays and the quantum normalization condition to constrain relic gravitational waves
• Analytic Spectra of CMB Anisotropies and Polarization Generated by Scalar Perturbations in Synchronous Gauge
• The propagating speed of relic gravitational waves and their refractive index during inflation
• Revisit relic gravitational waves based on the latest CMB observations
• Nonlinear Density Fluctuation Field Theory for Large Scale Structure
• The first observations of wide-band interferometers and the spectra of relic gravitons
• Point-splitting regularization of the stress tensor of a coupling scalar field in de Sitter space
• Testing inflationary consistency relations by the potential CMB observations
• Relic gravitational waves in the frame of slow-roll inflation with a power-law potential and the detection
• Second-order cosmological perturbations. III. Produced by scalar-scalar coupling during radiation-dominated stage
• Detection of relic gravitational waves in the CMB: Prospects for CMBPol mission
• Estimation of spectrum and parameters of relic gravitational waves using space-borne interferometers
• Fast scalar quadratic maximum likelihood estimators for the CMB B-mode power spectrum
• Pulsar Timing Residuals Induced by Gravitational Waves from Single Non-evolving Supermassive Black Hole Binaries with Elliptical Orbits
• Thermal gravitational-wave background in the general pre-inflationary scenario
• Statistical imprints of CMB B-type polarization leakage in an incomplete sky survey analysis
• Very high frequency gravitational waves from magnetars and gamma-ray burst
• Second-order cosmological perturbations produced by scalar-scalar coupling during inflation stage
• Characterization of Extragalactic Point-Sources on E- and B-mode Maps of the CMB Polarization
• On CMB B-modes and the Onset of Inflation
• Primordial vorticity and gradient expansion
• Tensor B mode and stochastic Faraday mixing
• An analytical approach to the CMB anisotropies in a Spatially Closed background
• Polarizations of CMB and the Hubble tension
• Initial Condition of Relic Gravitational Waves Constrained by LIGO S6 and Multiple Interferometers
• The equation and solution of 4-point correlation function of galaxies in Gaussian approximation and its parity-odd part
• Detecting relic gravitational waves in the CMB: A statistical bias
• Reionization process dependence of the ratio of CMB polarization power spectra at low-$\ell$