  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.
