Testing Large-Scale Structure Measurements Against Fisher Matrix Predictions

TL;DR

This paper compares galaxy survey measurements of BAO and RSD with Fisher matrix predictions, finding good agreement for BAO but discrepancies in RSD due to degeneracies and assumptions, highlighting the limits of current models.

Contribution

It provides a detailed comparison between observed measurements and Fisher matrix predictions, identifying causes of discrepancies in RSD predictions and assessing the effective signal extraction scale.

Findings

BAO measurements align with Fisher predictions.

RSD measurements deviate from predictions due to degeneracies.

Current data extract signal comparable to linear regime for k < 0.08 h/Mpc.

Abstract

We compare Baryonic Acoustic Oscillation (BAO) and Redshift Space Distortion (RSD) measurements from recent galaxy surveys with their Fisher matrix based predictions. Measurements of the position of the BAO signal lead to constraints on the comoving angular diameter distance $D_{M}$ and the Hubble distance $D_{H}$ that agree well with their Fisher matrix based expectations. However, RSD-based measurements of the growth rate $f \sigma_{8}$ do not agree with the predictions made before the surveys were undertaken, even when repeating those predictions using the actual survey parameters. We show that this is due to a combination of effects including degeneracies with the geometric parameters $D_{M}$ and $D_{H}$, and optimistic assumptions about the scale to which the linear signal can be extracted. We show that measurements using current data and large-scale modelling techniques extract an equivalent amount of signal to that in the linear regime for $k < 0.08 \,h\,{\rm Mpc}^{-1}$, remarkably independent of the sample properties and redshifts covered.