Optimal Weights For Measuring Redshift Space Distortions in Multi-tracer Galaxy Catalogues

TL;DR

This paper introduces an optimized weighting scheme for galaxy surveys that improves the measurement of redshift space distortions, reducing variance in key cosmological parameters by up to 36%.

Contribution

It develops a new method for computing optimal weights tailored to specific cosmological parameters, enhancing data analysis in galaxy clustering studies.

Findings

Optimized weights reduce variance in growth rate measurements by up to 36%.

Method tested on mock catalogues with known parameters and power spectrum.

Application to DESI survey data demonstrates practical effectiveness.

Abstract

Since the volume accessible to galaxy surveys is fundamentally limited, it is extremely important to analyse available data in the most optimal fashion. One way of enhancing the cosmological information extracted from the clustering of galaxies is by weighting the galaxy field. The most widely used weighting schemes assign weights to galaxies based on the average local density in the region (FKP weights) and their bias with respect to the dark matter field (PVP weights). They are designed to minimize the fractional variance of the galaxy power-spectrum. We demonstrate that the currently used bias dependent weighting scheme can be further optimized for specific cosmological parameters. We develop a procedure for computing the optimal weights and test them against mock catalogues for which the values of all fitting parameters, as well as the input power-spectrum are known. We show that by applying these weights to the joint power-spectrum of Emission Line Galaxies and Luminous Red Galaxies from the Dark Energy Spectroscopic Instrument survey, the variance in the measured growth rate parameter can be reduced by as much as 36 per cent.