PREPRINT
3D01B140-2677-44C7-9C46-880965A0CF2C

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

Shohei Saga, Teppei Okumura, Atsushi Taruya, Takuya Inoue
arXiv:2207.03454

Submitted on 7 July 2022

## 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 $10$-$30\phantom{\rule{0.167em}{0ex}}\mathrm{M}\mathrm{p}\mathrm{c}/h$, 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.

## Preprint

Comment: 16 pages, 7 figures

Subjects: Astrophysics - Cosmology and Nongalactic Astrophysics; General Relativity and Quantum Cosmology