The RSD Sorting Hat: Unmixing Radial Scales in Projection

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 naïve 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.

17 pages. 11 Figures. PRD submitted

References in corpus (18)

• Array Programming with NumPy
• The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Cosmological Implications from two Decades of Spectroscopic Surveys at the Apache Point observatory
• The DESI Experiment Part I: Science,Targeting, and Survey Design
• Wide-Field InfrarRed Survey Telescope-Astrophysics Focused Telescope Assets WFIRST-AFTA 2015 Report
• A test of the nature of cosmic acceleration using galaxy redshift distortions
• Extended Limber Approximation
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Anisotropic galaxy clustering in Fourier-space
• KiDS-450 + 2dFLenS: Cosmological parameter constraints from weak gravitational lensing tomography and overlapping redshift-space galaxy clustering
• Fast likelihood-free cosmology with neural density estimators and active learning
• Systematic Bias in Cosmic Shear: Beyond the Fisher Matrix
• Consistent Modeling of Velocity Statistics and Redshift-Space Distortions in One-Loop Perturbation Theory
• Probing dark energy with the shear-ratio geometric test
• Nuisance hardened data compression for fast likelihood-free inference
• 2-FAST: Fast and accurate computation of projected two-point functions
• Nonlinear Redshift-Space Distortions in the Harmonic-space Galaxy Power Spectrum
• The first shear measurements from precision weak lensing
• A semi-analytic model of pairwise velocity distribution between dark matter halos
• Anisotropic effective redshift and evolving clustering amplitude

Cited by in corpus (2)

• Exploring the expansion of the universe using the Grüneisen parameter
• The Covariance of Photometric and Spectroscopic Two-Point Statistics: Implications for Cosmological Parameter Inference