Rejuvenating the Matter Power Spectrum III: The Cosmology Sensitivity of
  Gaussianized Power Spectra
  It was recently shown that applying a Gaussianizing transform, such as a
logarithm, to the nonlinear matter density field extends the range of useful
applicability of the power spectrum by a factor of a few smaller. Such a
transform dramatically reduces nonlinearities in both the covariance and the
shape of the power spectrum. Here, analyzing Coyote Universe real-space dark
matter density fields, we investigate the consequences of these transforms for
cosmological parameter estimation. The power spectrum of the log-density
provides the tightest cosmological parameter error bars (marginalized or not),
giving a factor of 2-3 improvement over the conventional power spectrum in all
five parameters tested. For the tilt, n_s, the improvement reaches a factor of
5. Similar constraints are achieved if the log-density power spectrum and
conventional power spectrum are analyzed together. Rank-order Gaussianization
seems just as useful as a log transform to constrain n_s, but not other
parameters. Dividing the overdensity by its dispersion in few-Mpc cells, while
it diagonalizes the covariance matrix, does not seem to help with parameter
constraints. We also provide a code that emulates these power spectra over a
range of concordance cosmological models.
