New Perspective on Galaxy Clustering as a Cosmological Probe: General Relativistic Effects

TL;DR

This paper develops a comprehensive general relativistic framework for galaxy clustering analysis, accounting for relativistic effects on observed galaxy positions and redshifts, crucial for precise cosmological measurements.

Contribution

It introduces a gauge-invariant formalism linking observed galaxy fluctuations to matter distribution, including tensor and scalar contributions, enhancing theoretical consistency.

Findings

Computed angular auto-correlation of large-scale structure

Analyzed cross-correlation with CMB temperature anisotropies

Discussed potential detection of primordial gravity waves

Abstract

We present a general relativistic description of galaxy clustering in a FLRW universe. The observed redshift and position of galaxies are affected by the matter fluctuations and the gravity waves between the source galaxies and the observer, and the volume element constructed by using the observables differs from the physical volume occupied by the observed galaxies. Therefore, the observed galaxy fluctuation field contains additional contributions arising from the distortion in observable quantities and these include tensor contributions as well as numerous scalar contributions. We generalize the linear bias approximation to relate the observed galaxy fluctuation field to the underlying matter distribution in a gauge-invariant way. Our full formalism is essential for the consistency of theoretical predictions. As our first application, we compute the angular auto correlation of large-scale structure and its cross correlation with CMB temperature anisotropies. We comment on the possibility of detecting primordial gravity waves using galaxy clustering and discuss further applications of our formalism.