Beyond the plane-parallel approximation for redshift surveys

TL;DR

This paper analytically investigates wide angle effects in redshift space distortions, highlighting their impact on clustering measurements and proposing new estimators for power spectrum and bispectrum multipoles.

Contribution

It provides an analytical framework for modeling wide angle effects and introduces new estimators based on spherical Fourier-Bessel coefficients.

Findings

Quantified biases due to wide angle effects in clustering observables.

Clarified the relation between measurements and theoretical models.

Proposed estimators that separate angular and radial modes.

Abstract

Redshift space distortions privilege the location of the observer in cosmological redshift surveys, breaking the translational symmetry of the underlying theory. This violation of statistical homogeneity has consequences for the modeling of clustering observables, leading to what are frequently called `wide angle effects'. We study these effects analytically, computing their signature in the clustering of the multipoles in configuration and Fourier space. We take into account both physical wide angle contributions as well as the terms generated by the galaxy selection function. Similar considerations also affect the way power spectrum estimators are constructed. We quantify, in an analytical way the biases which enter and clarify the relation between what we measure and the underlying theoretical modeling. The presence of an angular window function is also discussed. Motivated by this analysis we present new estimators for the three dimensional Cartesian power spectrum and bispectrum multipoles written in terms of spherical Fourier-Bessel coefficients. We show how the latter have several interesting properties, allowing in particular a clear separation between angular and radial modes.