Relativistic distortions in galaxy density-ellipticity correlations: gravitational redshift and peculiar velocity effects

Abstract

We study relativistic effects, arising from the light propagation in an inhomogeneous universe. We particularly investigate the effects imprinted in a cross-correlation function between galaxy positions and intrinsic galaxy shapes (GI correlation). Considering the Doppler and gravitational redshift effects as major relativistic effects, we present an analytical model of the GI correlation function, from which we find that the relativistic effects induce non-vanishing odd multipole anisotropies. Focusing particularly on the dipole anisotropy, we show that the Doppler effect dominates at large scales, while the gravitational redshift effect originated from the halo potential dominates at the scales below $10$-$30\mathrm{Mpc}/h$, with the amplitude of the dipole GI correlation being positive over all the scales. Also, we newly derive the covariance matrix for the modelled GI dipole. Taking into account the full covariance, we estimate the signal-to-noise ratio and show that the GI dipole induced by the relativistic effects is detectable in future large-volume galaxy surveys. We discuss how the measurement of dipole GI correlation could be helpful to detect relativistic effects in combination with the conventional galaxy-galaxy cross correlation.

16 pages, 7 figures

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• Imprints of primordial magnetic fields on intrinsic alignments of galaxies
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• Extracting parity-violating gravitational waves from projected tidal force tensor in three dimensions
• A rising tide: Intrinsic alignments since the turn of the millennium
• Information content in anisotropic cosmological fields: Impact of different multipole expansion scheme for galaxy density and ellipticity correlations
• Synergy between CSST and third-generation gravitational-wave detectors: Inferring cosmological parameters using cross-correlation of dark sirens and galaxies
• Evidence for Intrinsic Galaxy Alignments in Ellipticity Autocorrelations out to $100h^{-1}\text{Mpc}$ from SDSS Galaxies with DESI Imaging