Optimising the measurement of relativistic distortions in large-scale structure

TL;DR

This paper develops an optimal estimator to measure relativistic distortions in galaxy surveys, significantly improving detection prospects of the dipolar signal caused by relativistic effects in large-scale structure.

Contribution

It introduces a new optimal estimator for the relativistic dipole in galaxy correlations, enhancing signal detection in current and future surveys.

Findings

Estimator increases signal-to-noise by up to 35%.

Forecasts detectability in SDSS, DESI, and simulations.

Relativistic dipole should be observable with proper methods.

Abstract

It has been shown recently that relativistic distortions generate a dipolar modulation in the two-point correlation function of galaxies. To measure this relativistic dipole it is necessary to cross-correlate different populations of galaxies with for example different luminosities or colours. In this paper, we construct an optimal estimator to measure the dipole with multiple populations. We show that this estimator increases the signal-to-noise of the dipole by up to 35 percent. Using 6 populations of galaxies, in a survey with halos and number densities similar to those of the millennium simulation, we forecast a cumulative signal-to-noise of 4.4. For the main galaxy sample of SDSS at low redshift z<0.2 our optimal estimator predicts a cumulative signal-to-noise of 2.4. Finally we forecast a cumulative signal-to-noise of 7.4 in the upcoming DESI survey. These forecasts indicate that with the appropriate choice of estimator the relativistic dipole should be detectable in current and future surveys.