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

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(NL) by reducing sample variance and also parameter degeneracies. To model the full use of the 3D information of galaxy clustering, we forecast f(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(NL) and the growth-rate exponent gamma, marginalized over standard A cold dark matter (ACDM) 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(NL)) by a factor of 3 to 12 thanks to large radial modes. With future wide-field and high-redshift photometric surveys like the LSST, the constraint sigma(f(NL)) < 1 could be achieved using linear angular multipoles up to l(min) similar or equal to 20. Compared to using galaxy autopower spectra only, joint analyses with CMB lensing could improve sigma(gamma) by a factor of 2 to 5 by reducing degeneracies with other parameters, especially the clustering bias. For future spectroscopic surveys like the DESI or Euclid, using linear scales, gamma could be constrained to 3% precision, assuming the GR fiducial value.