Semi-analytical Study on the Generic Degeneracy for Galaxy Clustering Measurements

TL;DR

This paper derives semi-analytical results on the degeneracy in galaxy clustering measurements using the galaxy power spectrum, forecasting measurement precisions for a Euclid-like survey.

Contribution

It introduces a semi-analytical approach to understand the degeneracy between key galaxy clustering observables and forecasts their measurement precision.

Findings

Galaxy surveys show a slight negative correlation between observables.

The measurement of $ar{R}$ is 3.7 to 4.7 times more precise than $ar{A}$.

Forecasts are based on Fisher matrix formalism for a Euclid-like survey.

Abstract

From the galaxy power spectrum in redshift space, we derive semi-analytical results on the generic degeneracy of galaxy clustering measurements. Defining the observables $\bar{A}= Gb\sigma_8$ and $\bar{R} = Gf\sigma_8$, (being $G$ the growth function, $b$ the bias, $f$ the growth rate, and $\sigma_8$ the amplitude of the power spectrum), we perform a Fisher matrix formalism to forecast the expected precision of these quantities for a Euclid-like survey. Among the results we found that galaxy surveys have generically a slightly negative correlation between $\bar{A}$ and $\bar{R}$, and they can always measure $\bar{R}$ about 3.7 to 4.7 times better than $\bar{A}$.