1112.3100 (A. Rassat et al.)

3D Spherical Analysis of Baryon Acoustic Oscillations    [PDF]

A. Rassat, A. Refregier

Baryon Acoustic Oscillations (BAOs) are oscillatory features in the galaxy power spectrum which are used as a standard rod to measure the cosmological expansion. These have been studied in Cartesian space (Fourier or real space) or in spherical harmonic 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. In this paper, we present 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 is purely radial and reduces to the Cartesian Fourier power spectrum. In the opposite limit of a thin shell, all the information is contained in the tangential modes described by the 2D spherical harmonic 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 also find that the BAOs radialise more rapidly than the full SFB power spectrum. Our results suggest that the first peak of the BAOs in SFB space can be measured as 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 may also be measured, however, for shallow surveys these may already be in the non-linear regime.

View original: http://arxiv.org/abs/1112.3100