Detecting Relativistic Doppler by Multi-Tracing a Single Galaxy Population

TL;DR

This paper proposes a multi-tracer method to detect the relativistic Doppler effect in galaxy clustering data, enhancing the potential to confirm general relativity on cosmological scales using upcoming survey data.

Contribution

It introduces an optimized multi-tracer approach using a single galaxy dataset to improve detection of the relativistic Doppler effect in large-scale structure surveys.

Findings

Optimal galaxy sample split enhances Doppler detection significance.

Forecasts indicate potential for significant detection with DESI-like samples.

Method improves the ability to test general relativity on large scales.

Abstract

New data from ongoing galaxy surveys, such as the $Euclid$ satellite and the Dark Energy Spectroscopic Instrument (DESI), are expected to unveil physics on the largest scales of our universe. Dramatically affected by cosmic variance, these scales are of interest to large-scale structure studies as they exhibit relevant corrections due to general relativity (GR) in the $n$-point statistics of cosmological random fields. We focus on the relativistic, sample-dependent Doppler contribution to the observed clustering of galaxies, whose detection will further confirm the validity of GR in cosmological regimes. Sample- and scale-dependent, the Doppler term is more likely to be detected via cross-correlation measurements, where it acts as an imaginary correction to the power spectrum of fluctuations in galaxy number counts. We present a method allowing us to exploit multi-tracer benefits from a single data set, by subdividing a galaxy population into two sub-samples, according to galaxies' luminosity/magnitude. To overcome cosmic variance we rely on a multi-tracer approach, and to maximise the detectability of the relativistic Doppler contribution in the data, we optimise sample selection. As a result, we find the optimal split and forecast the relativistic Doppler detection significance for both a DESI-like Bright Galaxy Sample and a $Euclid$-like H$\alpha$ galaxy population.