Gravitational redshift in the void-galaxy cross-correlation function in redshift space

TL;DR

This paper develops an analytic model to predict the gravitational redshift signal in the void-galaxy cross-correlation function in redshift space, enabling potential detection of gravitational potential within cosmic voids.

Contribution

It introduces the first theoretical model including second order velocity and potential effects to predict the dipole signal caused by gravitational redshift in voids.

Findings

The dipole is dominated by gravitational redshift, offering a new way to detect void potentials.

Higher order effects influence the quadrupole but are negligible for the monopole.

The model provides a new method for testing gravity and cosmology using voids.

Abstract

We construct an analytic model for the void-galaxy cross-correlation function that enables theoretical predictions of the dipole signal produced dominantly by the gravitational redshift within voids for the first time. By extending a theoretical formulation for the redshift-space distortion of galaxies to include the second order terms of the galaxy peculiar velocity $\bm v$ and the gravitational potential, we formulate the void-galaxy cross-correlation function multipoles in the redshift space, the monopole $\xi_0^{(s)}$, dipole $\xi_1^{(s)}$ and quadrupole $\xi_2^{(s)}$. We find that the dipole $\xi_1^{(s)}$ is dominated by the gravitational redshift, which provide a unique opportunity to detect the gravitational potential of voids. Thus, for the dipole $\xi_1^{(s)}(s)$, the gravitational redshift is crucial. Although the higher order effect is almost negligible on the monopole $\xi_0^{(s)}$, it has an influence on the quadrupole $\xi_2^{(s)}$. The effects from the random velocity of galaxies and the definition of the void center on the dipole signal are also discussed. Our model offers a new theoretical probe for the detection of gravitational redshift with voids and further tests on cosmology and gravity.