Large-scale Modeling of the Observed Power Spectrum Multipoles

TL;DR

This paper develops a precise theoretical framework for modeling large-scale power spectrum multipoles in galaxy surveys, accounting for wide-angle effects, redshift evolution, and observational constraints, validated with realistic mocks.

Contribution

It introduces a discrete spherical Fourier-Bessel basis for accurate, stable modeling of power spectrum multipoles on large scales, incorporating survey effects and validation with mocks.

Findings

Effective separation of angular and radial modes.

Accurate modeling of wide-angle and redshift evolution effects.

Validation with realistic survey geometries and mocks.

Abstract

Current and upcoming large-scale structure surveys are pushing toward increasingly wide angular coverage, where wide-angle effects (arising from the varying line of sight across the curved sky) become critical for accurate modeling of the three-dimensional galaxy power spectrum. At the same time, these survey's broader redshift reach makes the effects of redshift evolution (beyond the effective-redshift approximation) non-negligible on large radial scales. Additional observational effects such as the survey window function and integral constraints also become significant on these large scales, necessitating a careful theoretical treatment to robustly constrain local primordial non-Gaussianities and relativistic effects. In this work, we present a consistent and accurate theoretical framework for modeling the commonly used power spectrum multipoles (PSM) on large scales using the discrete spherical Fourier-Bessel (dSFB) basis. This basis ensures numerical stability and allows an exact separation between angular and radial modes. Using the dSFB basis, we study the impact of wide-angle effects and redshift evolution on the PSM, and incorporate the effects of window function convolution and integral constraints. We validate our PSM modeling using lognormal mocks under radial integral constraints with realistic survey geometries, demonstrating the readiness of our framework for application to all-sky galaxy surveys.