Rejuvenating the Matter Power Spectrum: Restoring Information With a Logarithmic Density Mapping

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 gives a power spectrum with a shape hardly departing from the linear power spectrum for k ≲ 1 h Mpc −1 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.