Non-linear relativistic contributions to the cosmological weak-lensing convergence

Abstract

Relativistic contributions to the dynamics of structure formation come in a variety of forms, and can potentially give corrections to the standard picture on typical scales of 100 Mpc. These corrections cannot be obtained by Newtonian numerical simulations, so it is important to accurately estimate the magnitude of these relativistic effects. Density fluctuations couple to produce a background of gravitational waves, which is larger than any primordial background. A similar interaction produces a much larger spectrum of vector modes which represent the frame-dragging rotation of spacetime. These can change the metric at the percent level in the concordance model at scales below the equality scale. Vector modes modify the lensing of background galaxies by large-scale structure. This gives in principle the exciting possibility of measuring relativistic frame dragging effects on cosmological scales. The effects of the non-linear tensor and vector modes on the cosmic convergence are computed and compared to first-order lensing contributions from density fluctuations, Doppler lensing, and smaller Sachs-Wolfe effects. The lensing from gravitational waves is negligible so we concentrate on the vector modes. We show the relative importance of this for future surveys such as Euclid and SKA. We find that these non-linear effects only marginally affect the overall weak lensing signal so they can safely be neglected in most analyses, though are still much larger than the linear Sachs-Wolfe terms. The second-order vector contribution can dominate the first-order Doppler lensing term at moderate redshifts and are actually more important for survey geometries like the SKA.

18 pages, 22 figures

References in corpus (17)

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Gravitational Wave Spectrum Induced by Primordial Scalar Perturbations
• The cosmological gravitational wave background from primordial density perturbations
• Extended Limber Approximation
• Accelerated expansion from structure formation
• A new framework for analyzing the effects of small scale inhomogeneities in cosmology
• Do stochastic inhomogeneities affect dark-energy precision measurements?
• Scale dependence of cosmological backreaction
• On the onset of cosmological backreaction
• Anti-lensing: the bright side of voids
• The cosmic microwave background bispectrum from the non-linear evolution of the cosmological perturbations
• The influence of structure formation on the cosmic expansion
• Cosmic microwave background bispectrum on small angular scales
• Vector modes generated by primordial density fluctuations
• Cosmic Shear from Scalar-Induced Gravitational Waves
• Late time anisotropy as an imprint of cosmological backreaction
• Spectral distortions in the cosmic microwave background polarization

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• Cosmology on all scales: a two-parameter perturbation expansion
• Effect of inhomogeneities on high precision measurements of cosmological distances
• The theory of stochastic cosmological lensing
• General and consistent statistics for cosmological observations
• General Relativistic Corrections to the Weak Lensing Convergence Power Spectrum
• Relativistic cosmological large scale structures at one-loop
• Weak-lensing $B$-modes as a probe of the isotropy of the universe
• Vector perturbations of galaxy number counts
• Lagrangian theory of structure formation in relativistic cosmology. IV. Lagrangian approach to gravitational waves
• Perturbation theory for cosmologies with non-linear structure
• Imprints of local lightcone projection effects on the galaxy bispectrum IV: Second-order vector and tensor contributions
• Looking for a twist: probing the cosmological gravitomagnetic effect via weak lensing-kSZ cross correlations
• The density distributions of cosmic structures: impact of the local environment on weak-lensing convergence
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• Weak lensing corrections to tSZ-lensing cross correlation
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