Observing relativistic features in large-scale structure surveys -- I: Multipoles of the power spectrum

TL;DR

This paper develops a relativistic analysis pipeline for large-scale structure surveys, focusing on the gauge-independent modeling of the power spectrum multipoles, especially the dipole, to detect potential signatures of relativistic effects beyond Newtonian approximations.

Contribution

It introduces a novel, fully relativistic, gauge-independent method to accurately model and recover relativistic spectra and correlation functions in large-scale structure surveys.

Findings

Successful extraction of the relativistic dipole in the power spectrum

Comparison of methods for accounting survey geometry and evolution effects

Insights into the detectability of GR signatures in future surveys

Abstract

Planned efforts to probe the largest observable distance scales in future cosmological surveys are motivated by a desire to detect relic correlations left over from inflation, and the possibility of constraining novel gravitational phenomena beyond General Relativity (GR). On such large scales, the usual Newtonian approaches to modelling summary statistics like the power spectrum and bispectrum are insufficient, and we must consider a fully relativistic and gauge-independent treatment of observables such as galaxy number counts in order to avoid subtle biases, e.g. in the determination of the $f_{\rm NL}$ parameter. In this work, we present an initial application of an analysis pipeline capable of accurately modelling and recovering relativistic spectra and correlation functions. As a proof of concept, we focus on the non-zero dipole of the redshift-space power spectrum that arises in the cross-correlation of different mass bins of dark matter halos, using strictly gauge-independent observable quantities evaluated on the past light cone of a fully relativistic N-body simulation in a redshift bin $1.7 \le z \le 2.9$. We pay particular attention to the correct estimation of power spectrum multipoles, comparing different methods of accounting for complications such as the survey geometry (window function) and evolution/bias effects on the past light cone, and discuss how our results compare with previous attempts at extracting novel GR signatures from relativistic simulations.