General Relativistic Description of the Observed Galaxy Power Spectrum: Do We Understand What We Measure?

TL;DR

This paper develops a fully general relativistic framework for describing the observed galaxy power spectrum, revealing significant differences from the Newtonian approach on large scales and emphasizing its importance for future high-redshift surveys.

Contribution

It provides the first comprehensive general relativistic description of the observed galaxy power spectrum, accounting for large-scale effects and redshift evolution.

Findings

Standard Newtonian description is adequate at low redshift.

Relativistic effects can mimic primordial non-Gaussianity.

Correct modeling is crucial for future surveys with z>3.

Abstract

We extend the general relativistic description of galaxy clustering developed in Yoo, Fitzpatrick, and Zaldarriaga (2009). For the first time we provide a fully general relativistic description of the observed matter power spectrum and the observed galaxy power spectrum with the linear bias ansatz. It is significantly different from the standard Newtonian description on large scales and especially its measurements on large scales can be misinterpreted as the detection of the primordial non-Gaussianity even in the absence thereof. The key difference in the observed galaxy power spectrum arises from the real-space matter fluctuation defined as the matter fluctuation at the hypersurface of the observed redshift. As opposed to the standard description, the shape of the observed galaxy power spectrum evolves in redshift, providing additional cosmological information. While the systematic errors in the standard Newtonian description are negligible in the current galaxy surveys at low redshift, correct general relativistic description is essential for understanding the galaxy power spectrum measurements on large scales in future surveys with redshift depth z>3. We discuss ways to improve the detection significance in the current galaxy surveys and comment on applications of our general relativistic formalism in future surveys.