The RSD Sorting Hat: Unmixing Radial Scales in Projection

TL;DR

This paper investigates how to optimally extract redshift space distortion information from projected data, proposing a new radial weighting scheme that improves constraints while minimizing model bias for joint RSD and weak lensing analyses.

Contribution

It introduces a novel radial weighting scheme that unmixes radial RSD scales in projection, enabling more effective joint RSD and weak lensing studies.

Findings

Naive tomographic projection mixes large and nonlinear scales, reducing constraint effectiveness.

The new weighting scheme unmixes radial RSD scales, improving constraints.

The proposed method maintains low model bias even with narrow tomographic bins.

Abstract

Future data sets will enable cross-correlations between redshift space distortions (RSD) and weak lensing (WL). While photometric lensing and clustering cross-correlations have provided some of the tightest cosmological constraints to date, it is not well understood how to optimally perform similar RSD/WL joint analyses in a lossless way. RSD is typically measured in $3D$ redshift space, but WL is inherently a projected signal, making angular statistics a natural choice for the combined analysis. Thus, we determine the amount of RSD information that can be extracted using projected statistics. Specifically we perform a Fisher analysis to forecast constraints and model bias comparing two different Fingers-of-God (FoG) models using both, the $3D$ power spectrum, $P(k, \mu)$, and tomographic $C(\ell)$. We find that because na\"ive tomographic projection mixes large scales with poorly modelled nonlinear radial modes, it does not provide competitive constraints to the $3D$ RSD power spectrum without the model bias becoming unacceptably large. This is true even in the limit of narrow tomographic bins. In light of this we propose a new radial weighting scheme which unmixes radial RSD scales in projection yielding competitive constraints to the $3D$ RSD power spectrum, while keeping the model bias small. This work lays the groundwork for optimal joint analyses of RSD and cosmic shear.