A case study for measuring the relativistic dipole of a galaxy cross-correlation with the Dark Energy Spectroscopic Instrument

TL;DR

This study assesses the potential to detect the relativistic dipole in galaxy cross-correlation data from DESI, showing that with optimal galaxy population splits, detection significance can reach 19 sigma, confirming theoretical predictions.

Contribution

It provides an independent evaluation of the relativistic dipole detectability in DESI galaxy data using synthetic catalogs and explores optimal galaxy population splits for enhanced detection.

Findings

Detectability reaches 19 sigma with an unequal bright-faint galaxy split.

Measured dipole matches linear theory predictions down to 30 Mpc/h.

Optimal galaxy selection boosts relativistic dipole detection significance.

Abstract

The data on spectroscopic galaxy clustering collected by the Dark Energy Spectroscopic Instrument (DESI) will allow the significant detection of subtle features in the galaxy two-point correlation in redshift space, beyond the "standard" redshift-space distortions. Here we present an independent assessment of the detectability of the relativistic dipole in the cross-correlation of two populations of galaxies if they would be selected from the Bright Galaxy Survey (BGS) of DESI. We build synthetic galaxy catalogues with the characteristics of the BGS using the light cone of a relativistic $N$-body simulation. Exploring different ways of splitting the populations of galaxies we find that with an unequal split with more bright galaxies than faint galaxies the detectability is significantly boosted, reaching 19 $\sigma$ in the redshift bin $0.2 \lesssim z \lesssim 0.3$ and expected to be even higher at lower redshift. Moreover, we find that the measured dipole agrees very well with the prediction of relativistic effects from linear theory down to separations of $\sim$ 30 Mpc/$h$.