Two-point correlation function of density perturbations in a large void universe

TL;DR

This paper investigates the two-point correlation function of density perturbations in a spherically symmetric void universe, revealing local anisotropy caused by tidal forces, which could be tested through galaxy surveys.

Contribution

It introduces a method to compute the two-point correlation function in an inhomogeneous universe without assuming the Copernican principle, highlighting anisotropic effects.

Findings

Two-point correlation function exhibits local anisotropy off-center.

Anisotropy is caused by tidal forces in the void's off-center region.

Potential observational test via galaxy correlation function distortions.

Abstract

We study the two-point correlation function of density perturbations in a spherically symmetric void universe model which does not employ the Copernican principle. First we solve perturbation equations in the inhomogeneous universe model and obtain density fluctuations by using a method of non-linear perturbation theory which was adopted in our previous paper. From the obtained solutions, we calculate the two-point correlation function and show that it has a local anisotropy at the off-center position differently from those in homogeneous and isotropic universes. This anisotropy is caused by the tidal force in the off-center region of the spherical void. Since no tidal force exists in homogeneous and isotropic universes, we may test the inhomogeneous universe by observing statistical distortion of the two-point galaxy correlation function.