  The power spectrum is widely used in astronomy, to analyze temporal or
spatial structure. In cosmology, it is used to quantify large-scale structure
(LSS) and the cosmic microwave background (CMB). This is because the power
spectrum completely quantifies Gaussian random fields, which the CMB and LSS
fields seem to be at early epochs. However, at late epochs and small scales,
cosmological density fields become highly non-Gaussian. The power spectrum
loses power to describe LSS and CMB fields on small scales, most obviously
through high covariance in the power spectrum as a function of scale.
Practically, this significantly degrades constraints that observations can
place on cosmological parameters. However, if a nonlinear transformation that
produces a (more) Gaussian 1-point distribution is applied to a field, the
extra covariance in the field's power spectrum can be dramatically reduced. In
the case of the roughly lognormal low-redshift matter density field, a log
transform accomplishes this. Applying a log transform to the density field
before measuring the power spectrum also tightens cosmological parameter
constraints by a factor of several.
