Vector perturbations of galaxy number counts

TL;DR

This paper derives the effects of vector and tensor perturbations on relativistic galaxy number counts, extending the understanding of relativistic corrections beyond scalar perturbations and providing numerical estimates for their impact.

Contribution

It presents a derivation of relativistic galaxy number count fluctuations from vector and tensor perturbations, including second-order induced vector perturbations and their numerical impact.

Findings

Vector and tensor perturbations contribute to galaxy number counts without density fluctuations.

The derived formulas are consistent with scalar perturbation corrections, replacing Bardeen potentials with line-of-sight projections.

Numerical estimates show the magnitude of these contributions to the power spectrum.

Abstract

We derive the contribution to relativistic galaxy number count fluctuations from vector and tensor perturbations within linear perturbation theory. Our result is consistent with the the relativistic corrections to number counts due to scalar perturbation, where the Bardeen potentials are replaced with line-of-sight projection of vector and tensor quantities. Since vector and tensor perturbations do not lead to density fluctuations the standard density term in the number counts is absent. We apply our results to vector perturbations which are induced from scalar perturbations at second order and give numerical estimates of their contributions to the power spectrum of relativistic galaxy number counts.