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

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 $f_{\mathrm{NL}}$ by reducing sample variance and also parameter degeneracies. To model the full use of the 3D information of galaxy clustering, we forecast $f_{\mathrm{NL}}$ 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 $f_{\mathrm{NL}}$ 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 $\sigma (f_{\mathrm{NL}})$ by factors 3 to 12 thanks to large radial modes. With future wide-field and high-redshift photometric surveys like the LSST, the constraint $\sigma (f_{\mathrm{NL}})<1$ could be achieved using linear angular multipoles up to ${\ell }_{\min }\simeq 20$. 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 $\text{Euclid}$, using linear scales, $\gamma$ could be constrained to $3\%$ precision assuming the GR fiducial value.

21 pages, 14 figures, 3 tables; references added, published in PRD

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Cited by in corpus (5)

• Wide-angle and relativistic effects in Fourier-space clustering statistics
• The full-sky Spherical Fourier-Bessel power spectrum in general relativity
• Exact Modeling of Power Spectrum Multipole through Spherical Fourier-Bessel Basis
• Linear Relativistic Corrections in the Spherical Fourier-Bessel Power Spectrum
• The Covariance of Photometric and Spectroscopic Two-Point Statistics: Implications for Cosmological Parameter Inference