Ringing the initial Universe: the response of overdensity and
  transformed-density power spectra to initial spikes
  We present an experiment in which we 'ring' a set of cosmological
N-body-simulation initial conditions, placing spikes in the initial power
spectrum at different wavenumber bins. We then measure where these spikes end
up in the final conditions. In the usual overdensity power spectrum, most
sensitive to contracting and collapsing dense regions, initial power on
slightly non-linear scales (k ~ 0.3 h/Mpc) smears to smaller scales, coming to
dominate the initial power once there. Log-density and Gaussianized-density
power spectra, sensitive to low-density (expanding) and high-density regions,
respond differently: initial spikes spread symmetrically in scale, both upward
and downward. In fact, in the power spectrum of 1/(1 + {\delta}), spikes
migrate to larger scales, showing the magnifying effect of voids on small-scale
modes. These power spectra show much greater sensitivity to small-scale initial
features. We also test the difference between an approximation of the
Ly-{\alpha} flux field, and its Gaussianized form, and give a toy model that
qualitatively explains the symmetric power spreading in Gaussianized-density
power spectra. Also, we discuss how to use this framework to estimate
power-spectrum covariance matrices. This can be used to track the fate of
information in the Universe, that takes the form of initial degrees of freedom,
one random spike per initial mode.
