Relativistic Effect in Galaxy Clustering

TL;DR

This paper reviews the relativistic effects in galaxy clustering, emphasizing their importance on large scales for testing gravity theories and understanding the early Universe, through a pedagogical derivation and analysis of observed statistics.

Contribution

It provides a comprehensive, gauge-invariant relativistic framework for galaxy clustering, addressing gauge issues and deriving observable two-point statistics.

Findings

Relativistic effects are significant on large scales.

The gauge-invariant formula improves accuracy in galaxy clustering analysis.

Relativistic description aids in testing gravity and early Universe models.

Abstract

The general relativistic description of galaxy clustering provides a complete and unified treatment of all the effects in galaxy clustering such as the redshift-space distortion, gravitational lensing, Sachs-Wolfe effects, and their relativistic effects. In particular, the relativistic description resolves the gauge issues in the standard Newtonian description of galaxy clustering by providing the gauge-invariant expression for the observed galaxy number density. The relativistic effect in galaxy clustering is significant on large scales, in which dark energy models or alternative theories of modified gravity deviate from general relativity. In this paper, we review the relativistic effect in galaxy clustering by providing a pedagogical derivation of the relativistic formula and by computing the observed galaxy two-point statistics. The relativistic description of galaxy clustering is an essential tool for testing general relativity and probing the early Universe on large scales in the era of precision cosmology.