  Upcoming spectroscopic galaxy surveys are extremely promising to help in
addressing the major challenges of cosmology, in particular in understanding
the nature of the dark universe. The strength of these surveys comes from their
unprecedented depth and width. Optimal extraction of their three-dimensional
information is of utmost importance to best constrain the properties of the
dark universe. Although there is theoretical motivation and novel tools to
explore these surveys using the 3D spherical Fourier-Bessel (SFB) power
spectrum of galaxy number counts $C_\ell(k,k^\prime)$, most survey
optimisations and forecasts are based on the tomographic spherical harmonics
power spectrum $C^{(ij)}_\ell$. We performed a new investigation of the
information that can be extracted from the tomographic and 3D SFB techniques by
comparing the forecast cosmological parameter constraints obtained from a
Fisher analysis in the context of planned stage IV wide-field galaxy surveys.
The comparison was made possible by careful and coherent treatment of
non-linear scales in the two analyses. Nuisance parameters related to a scale-
and redshift-dependent galaxy bias were also included for the first time in the
computation of both the 3D SFB and tomographic power spectra. Tomographic and
3D SFB methods can recover similar constraints in the absence of systematics.
However, constraints from the 3D SFB analysis are less sensitive to unavoidable
systematics stemming from a redshift- and scale-dependent galaxy bias. Even for
surveys that are optimised with tomography in mind, a 3D SFB analysis is more
powerful. In addition, for survey optimisation, the figure of merit for the 3D
SFB method increases more rapidly with redshift, especially at higher
redshifts, suggesting that the 3D SFB method should be preferred for designing
and analysing future wide-field spectroscopic surveys.
