Hybrid-basis inference for large-scale galaxy clustering: combining spherical and Cartesian Fourier analyses

TL;DR

This paper introduces a hybrid Fourier basis approach for large-scale galaxy clustering analysis, combining spherical and Cartesian methods to improve cosmological constraints on very large scales.

Contribution

It proposes a novel hybrid basis method that combines spherical and Cartesian Fourier analyses, addressing limitations of previous approaches on large scales.

Findings

Effective in modeling large-scale clustering with spherical modes.

Compatible with likelihood analysis of primordial non-Gaussianity.

Public code Harmonia released for community use.

Abstract

Future precision cosmology from large-scale structure experiments including the Dark Energy Spectroscopic Instrument (DESI) and Euclid will probe wider and deeper cosmic volumes than those covered by previous surveys. The Cartesian power spectrum analysis of anisotropic galaxy clustering based on the Fourier plane wave basis makes a number of assumptions, including the local plane-parallel approximation, that will no longer be valid on very large scales and may degrade cosmological constraints. We propose an approach that utilises a hybrid basis: on the largest scales, clustering statistics are decomposed into spherical Fourier modes which respect the natural geometry of both survey observations and physical effects along the line of sight, such as redshift-space distortions, the Alcock--Paczy\'nsky and light-cone effects; on smaller scales with far more clustering modes, we retain the computational benefit of the power spectrum analysis aided by fast Fourier transforms. This approach is particularly suited to the likelihood analysis of local primordial non-Gaussianity $f_\textrm{NL}$ through the scale-dependent halo bias, and we demonstrate its applicability with $N$-body simulations. We also release our public code Harmonia (https://github.com/MikeSWang/Harmonia) for galaxy clustering likelihood inference in spherical Fourier or hybrid-basis analyses.