Precision Prediction of the Log Power Spectrum

Abstract: At translinear scales, the log power spectrum captures significantly more cosmological information than the standard power spectrum. At high wavenumbers $k$, the Fisher information in the standard power spectrum $P(k)$ fails to increase in proportion to $k$ in part due to correlations between large- and small-scale modes. As a result, $P(k)$ suffers from an information plateau on these translinear scales, so that analysis with the standard power spectrum cannot access the information contained in these small-scale modes. The log power spectrum $P_A(k)$, on the other hand, captures the majority of this otherwise lost information. Until now there has been no means of predicting the amplitude of the log power spectrum apart from cataloging the results of simulations. We here present a cosmology-independent prescription for the log power spectrum; this prescription displays accuracy comparable to that of Smith et al. (2003), over a range of redshifts and smoothing scales, and for wavenumbers up to $1.5h$ Mpc$^{-1}$.