Linear Relativistic Corrections in the Spherical Fourier-Bessel Power Spectrum

TL;DR

This paper derives the linear relativistic galaxy power spectrum in the spherical Fourier-Bessel basis, accounting for wide-angle and GR effects, and compares these effects to primordial non-Gaussianity signals for large-scale structure surveys.

Contribution

It introduces a method to compute the relativistic power spectrum in the SFB basis, including GR effects, and validates it against CLASS outputs, highlighting the potential to distinguish GR effects from PNG.

Findings

GR effects have distinct angular and Fourier signatures in the SFB basis.

The gravitational potential term mimics a PNG signal of f_NL ~ 1.

Lensing effects can potentially be extracted from SFB modes in future surveys.

Abstract

The three-dimensional galaxy power spectrum is a powerful probe of primordial non-Gaussianity and additional general relativistic (GR) effects on large scales, which can be constrained by the current and upcoming large-scale structure surveys. In this work, we calculate the linear-order relativistic power spectrum in the spherical Fourier-Bessel (SFB) basis, a coordinate system that preserves the geometry of the curved sky and fully accounts for the wide-angle effect. In particular, we model the GR effects present in the discrete SFB power spectrum, which is a more efficient and stable decomposition of the galaxy density field compared to the continuous SFB basis in the presence of radial windows. To validate our GR calculations, we introduce a mapping between the angular power spectrum and the SFB power spectrum, and we compare our calculations with outputs from CLASS. We discuss the rich pattern of GR effects in the SFB basis and compare the GR effects to the local primordial non-Gaussianity (PNG) effect. The Doppler and lensing effects have different angular and Fourier dependence compared to the PNG in the SFB basis, while the gravitational potential term is more degenerate with the PNG and comparable to a signal of $f_{\rm NL}\sim 1$. We also discuss the potential opportunities of extracting the lensing effect through SFB modes in upcoming LSS surveys.