Rejuvenating the matter power spectrum: restoring information with a logarithmic density mapping

TL;DR

Applying a logarithmic transformation to the dark-matter density field significantly reduces nonlinear distortions in the power spectrum, revealing more linear-like behavior and increasing the available Fisher information across scales.

Contribution

This study demonstrates that a logarithmic density mapping restores linearity and enhances information content in the matter power spectrum, improving analysis of cosmological data.

Findings

Nonlinearities are dramatically reduced after logarithmic mapping.

Power spectrum shape remains close to linear for k <~ 1 h/Mpc across redshifts.

Fisher information is increased by a factor of 2-3, with tenfold more cumulative signal-to-noise at z=0.

Abstract

We find that nonlinearities in the dark-matter power spectrum are dramatically smaller if the density field first undergoes a logarithmic mapping. In the Millennium simulation, this procedure produces a power spectrum with a shape hardly departing from the linear power spectrum for k <~ 1 h/Mpc at all redshifts. Also, this procedure unveils pristine Fisher information on a range of scales reaching a factor of 2-3 smaller than in the standard power spectrum, yielding 10 times more cumulative signal-to-noise at z=0.