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. 
Mark C. Neyrinck (JHU)
astro-ph.CO