Weak Lensing of the Cosmic Microwave Background by Foreground Gravitational Waves

Abstract

Weak lensing distortion of the background cosmic microwave background (CMB) temperature and polarization patterns by the foreground density fluctuations is well studied in the literature. We discuss the gravitational lensing modification to CMB anisotropies and polarization by a stochastic background of primordial gravitational waves between us and the last scattering surface. While density fluctuations perturb CMB photons via gradient-type deflections only, foreground gravitational waves distort CMB anisotropies via both gradient- and curl-type displacements. The latter is a rotation of background images, while the former is related to the lensing convergence. For a primordial background of inflationary gravitational waves, with an amplitude corresponding to a tensor-to-scalar ratio below the current upper limit of $\sim$ 0.3, the resulting modifications to the angular power spectra of CMB temperature anisotropy and polarization are below the cosmic variance limit. At tens of arcminute angular scales and below, these corrections, however, are above the level at which systematics must be controlled in all-sky anisotropy and polarization maps with no instrumental noise and other secondary and foreground signals.

arXiv comment11 pages, 4 figures; Revised version updates the numerical calculation for several corrections to the analytical formulation of lensing by foreground gravitational waves. Main conclusions unchanged. Version accepted for publication in Phys. Rev. D

References in corpus (25)

• Weak Gravitational Lensing
• Weak Gravitational Lensing of the CMB
• Signature of Gravity Waves in Polarization of the Microwave Background
• A Probe of Primordial Gravity Waves and Vorticity
• Mass Reconstruction with CMB Polarization
• Gravitational Lensing Effect on Cosmic Microwave Background Polarization
• CMB Lensing Reconstruction on the Full Sky
• Weak Lensing of the CMB: A Harmonic Approach
• Reconstruction of lensing from the cosmic microwave background polarization
• A limit on the detectability of the energy scale of inflation
• The Angular Trispectrum of the CMB
• Gravitational lensing as a contaminant of the gravity wave signal in CMB
• Separation of Gravitational-Wave and Cosmic-Shear Contributions to Cosmic Microwave Background Polarization
• Reconstructing Projected Matter Density from Cosmic Microwave Background
• Cosmic Microwave Background Fluctuations from Gravitational Waves: An Analytic Approach
• Lensing Reconstruction with CMB Temperature and Polarization
• Second Order Corrections to Weak Lensing by Large-Scale Structure
• Measuring Dark Matter Power Spectrum from Cosmic Microwave Background
• Primordial Gravity Waves and Weak Lensing
• Direct Signature of Evolving Gravitational Potential from Cosmic Microwave Background
• Cosmic Shear of the Microwave Background: The Curl Diagnostic
• Bending of Light by Gravity Waves
• Gravitational Time Delay Effects on CMB Anisotropies
• Geometry of weak lensing of CMB polarization
• The Born and Lens-Lens Corrections to Weak Gravitational Lensing Angular Power Spectra

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• Primordial Gravitational Waves from Axion-Gauge Fields Dynamics
• Impact of post-Born lensing on the CMB
• Imprints of Massive Primordial Fields on Large-Scale Structure
• Inflationary tensor fossils in large-scale structure
• Anisotropic imprint of long-wavelength tensor perturbations on cosmic structure
• Full-sky lensing reconstruction of gradient and curl modes from CMB maps
• Lensing of 21-cm Fluctuations by Primordial Gravitational Waves
• Total Angular Momentum Waves for Scalar, Vector, and Tensor Fields
• Inflation and Early Dark Energy with a Stage II Hydrogen Intensity Mapping Experiment
• Testing statistics of the CMB B-mode polarization toward unambiguously establishing quantum fluctuation of vacuum
• Odd-Parity Bipolar Spherical Harmonics
• Cosmic Shear from Scalar-Induced Gravitational Waves
• Weak lensing induced by second-order vector mode
• Weak lensing generated by vector perturbations and detectability of cosmic strings
• Full-sky formulae for weak lensing power spectra from total angular momentum method
• A Constraint On the Integrated Mass Power Spectrum out to z = 1100 from Lensing of the Cosmic Microwave Background
• Rotation of the cosmic microwave background polarization from weak gravitational lensing
• Non-Gaussian Covariance of CMB B-modes of Polarization and Parameter Degradation
• Lensing signals from Spin-2 perturbations
• A New Window into Stochastic Gravitational Wave Background
• Future detectability of gravitational-wave induced lensing from high-sensitivity CMB experiments
• Imprints of primordial magnetic fields on intrinsic alignments of galaxies
• Unified approach to secondary effects on the CMB B-mode polarization
• A comparison of CMB lensing efficiency of gravitational waves and large scale structure
• Establishing the origin of CMB B-mode polarization
• The imprint of primordial gravitational waves on the CMB intensity profile
• Constraining stochastic gravitational wave background from weak lensing of CMB B-modes
• Weak lensing from self-ordering scalar fields