Joint analyses of 2D CMB lensing and 3D galaxy clustering in the spherical Fourier-Bessel basis

TL;DR

This paper demonstrates that combining 2D CMB lensing with 3D galaxy clustering in the spherical Fourier-Bessel basis significantly enhances constraints on primordial non-Gaussianity and gravity parameters, leveraging future survey data.

Contribution

It introduces a novel SFB decomposition method for joint analysis of CMB lensing and galaxy clustering, improving parameter constraints over traditional tomographic approaches.

Findings

SFB analysis improves $f_{NL}$ constraints by factors 3 to 12.

Joint analysis with CMB lensing enhances growth rate ($eta$) constraints by factors 2 to 5.

Future surveys could achieve $\sigma(f_{NL}) < 1$ with high-redshift data.

Abstract

Cross-correlating cosmic microwave background (CMB) lensing and galaxy clustering has been shown to greatly improve the constraints on the local primordial non-Gaussianity (PNG) parameter $f_{\rm NL}$ by reducing sample variance and also parameter degeneracies. To model the full use of the 3D information of galaxy clustering, we forecast $f_{\rm NL}$ measurements using the decomposition in the spherical Fourier-Bessel (SFB) basis, which can be naturally cross-correlated with 2D CMB lensing in spherical harmonics. In the meantime, such a decomposition would also enable us to constrain the growth rate of structure, a probe of gravity, through the redshift-space distortion (RSD). As a comparison, we also consider the tomographic spherical harmonic (TSH) analysis of galaxy samples with different bin sizes. Assuming galaxy samples that mimic a few future surveys, we perform Fisher forecasts using linear modes for $f_{\rm NL}$ and the growth rate exponent $\gamma$, marginalized over standard $\Lambda$ cold dark matter ($\Lambda$CDM) cosmological parameters and two nuisance parameters that account for clustering bias and magnification bias. Compared to TSH analysis using only one bin, SFB analysis could improve $\sigma(f_{\rm NL})$ by factors 3 to 12 thanks to large radial modes. With future wide-field and high-redshift photometric surveys like the LSST, the constraint $\sigma(f_{\rm NL}) < 1$ could be achieved using linear angular multipoles up to $\ell_{\rm min}\simeq 20$. Compared to using galaxy auto-power spectra only, joint analyses with CMB lensing could improve $\sigma(\gamma)$ by factors 2 to 5 by reducing degeneracies with other parameters, especially the clustering bias. For future spectroscopic surveys like the DESI or $\textit{Euclid}$, using linear scales, $\gamma$ could be constrained to $3\,\%$ precision assuming the GR fiducial value.