3D Spherical Analysis of Baryon Acoustic Oscillations
  Baryon Acoustic Oscillations (BAOs) are oscillatory features in the galaxy
power spectrum and are a standard rod to measure the cosmological expansion.
These have been studied in Cartesian space (Fourier or real space) or in
Spherical Harmonic (SH) space in thin shells. Future wide-field surveys will
cover both wide and deep regions of the sky and thus require a simultaneous
treatment of the spherical sky and of an extended radial coverage. The
Spherical Fourier-Bessel (SFB) decomposition is a natural basis for the
analysis of fields in this geometry and facilitates the combination of BAO
surveys with other cosmological probes readily described in this basis. We
present here a new way to analyse BAOs by studying the BAO wiggles from the SFB
power spectrum. In SFB space, the power spectrum generally has both a radial
(k) and tangential (l) dependence and so do the BAOs. In the deep survey limit
and ignoring evolution, the SFB power spectrum becomes radial and reduces to
the Cartesian Fourier power spectrum. In the limit of a thin shell, all the
information is contained in the tangential modes described by the 2D SH power
spectrum. We find that the radialisation of the SFB power spectrum is still a
good approximation even when considering an evolving and biased galaxy field
with a finite selection function. This effect can be observed by all-sky
surveys with depths comparable to current surveys. We find that the BAOs
radialise more rapidly than the full SFB power spectrum. Our results suggest
the first peak of the BAOs in SFB space becomes radial out to l ~ 10 for
all-sky surveys with the same depth as SDSS or 2dF, and out to l ~ 70 for an
all-sky stage IV survey. Subsequent BAO peaks also become radial, but for
shallow surveys these may be in the non-linear regime. For modes that have
become radial, measurements at different l's are useful in practice to reduce
measurement errors.
