Lifting the degeneracy between geometric and dynamic distortions using the sound horizon from the cosmic microwave background

Abstract

The degeneracy between geometric (Alcock-Paczynski) and dynamic (redshift-space) distortions in the pattern of the galaxy distribution has been a long-standing problem in the study of the large-scale structure of the Universe. We examine the possibility of lifting this degeneracy and constraining cosmological parameters by using the baryon acoustic oscillation (BAO) scale as a feature of known physical size, the sound horizon rs≈ 150Mpc. We calibrate this scale with the equivalent feature in the cosmic microwave background (CMB). First, we construct a toy model of a power spectrum which includes the BAO as well as geometric and dynamic distortions. By adding a prior on to the sound horizon of ∼1 per cent we show, using a Fisher matrix analysis, that error ellipses for line-of-sight and tangential distortion parameters shrink by a factor of 2 for a 20(h-1Gpc)3'DESpec/BigBOSS'-like galaxy survey including shot noise. This improvement is even more marked in smaller surveys. We also carry out a Monte Carlo nested sampling analysis on our parameter space. We find that Monte Carlo and Fisher methods can agree reasonably well for surveys with large volume but differ greatly for small volume surveys. © 2012 The Authors Monthly Notices of the Royal Astronomical Society © 2012 RAS.