Reducing the Variance of Redshift Space Distortion Measurements from Mock Galaxy Catalogues with Different Lines of Sight

TL;DR

This paper investigates how averaging over multiple lines of sight in mock galaxy catalogues reduces variance in redshift space distortion measurements, improving cosmological parameter precision efficiently.

Contribution

It derives an analytical expression for the covariance between measurements along different lines of sight and demonstrates variance reduction through averaging, enhancing RSD analysis accuracy.

Findings

Variance on the average measurement is reduced by over 1/3 with three LOS.

Averaging improves the precision of $f\sigma_8$ measurements by more than 1/3.

The method requires less than three times the CPU time of single LOS analysis.

Abstract

Accurate mock catalogues are essential for assessing systematics in the cosmological analysis of large galaxy surveys. Anisotropic two-point clustering measurements from the same simulation show some scatter for different lines of sight (LOS), but are on average equal, due to cosmic variance. This results in scatter in the measured cosmological parameters. We use the OuterRim N-body simulation halo catalogue to investigate this, considering the 3 simulation axes as LOS. The quadrupole of the 2-point statistics is particularly sensitive to changes in the LOS, with sub-percent level differences in the velocity distributions resulting in ~1.5$\sigma$ shifts on large scales. Averaging over multiple LOS can reduce the impact of cosmic variance. We derive an expression for the Gaussian cross-covariance between the power spectrum multipole measurements, for any two LOS, including shot noise, and the corresponding reduction in variance in the average measurement. Quadrupole measurements are anti-correlated, and for three orthogonal LOS, the variance on the average measurement is reduced by more than 1/3. We perform a Fisher analysis to predict the corresponding gain in precision on the cosmological parameter measurements, which we compare against a set of 300 extended Baryon Oscillation Spectroscopic Survey (eBOSS) emission line galaxy (ELG) EZmocks. The gain in $f\sigma_8$, which measures the growth of structure, is also better than 1/3. Averaging over multiple LOS in future mock challenges will allow the RSD models to be constrained with the same systematic error, with less than 3 times the CPU time.