On the total cosmological information in galaxy clustering: an
  analytical approach
  Beyond the linear regime of structure formation, part of cosmological
information encoded in galaxy clustering becomes inaccessible to the usual
power spectrum. "Sufficient statistics", A*, were introduced recently to
recapture the lost, and ultimately extract all, cosmological information. We
present analytical approximations for the A* and traditional power spectra as
well as for their covariance matrices in order to calculate analytically their
cosmological information content in the context of Fisher information theory.
Our approach allows the precise quantitative comparison of the techniques with
each other and to the total information in the data, and provides insights into
sufficient statistics. In particular, we find that while the A* power spectrum
has a similar shape to the usual galaxy power spectrum, its amplitude is
strongly modulated by small scale statistics. This effect is mostly responsible
for the ability of the A* power spectrum to recapture the information lost for
the usual power spectrum. We use our framework to forecast the best achievable
cosmological constraints for projected surveys as a function of their galaxy
density, and compare the information content of the two power spectra. We find
that sufficient statistics extract all cosmological information, resulting in
an approximately factor of ~2 gain for dense projected surveys at low redshift.
This increase in the effective volume of projected surveys is consistent with
previous numerical calculations.
