Calibrating the BAO scale using the CMB: Lifting the degeneracy between
  geometric and dynamic distortions using the sound horizon from the CMB
  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 r_s ~ 150 Mpc. We
callibrate 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 onto the sound horizon of ~1% we show, using a Fisher matrix analysis,
that error ellipses for line of sight and tangential distortion parameters
shrink by a factor of two for a 20(Gpc/h)^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.
