Perturbative Gaussianizing transforms for cosmological fields
  Constraints on cosmological parameters from large-scale structure have
traditionally been obtained from two-point statistics. However, non-linear
structure formation renders these statistics insufficient in capturing the full
information content available, necessitating the measurement of higher-order
moments to recover information which would otherwise be lost. We construct
quantities based on non-linear and non-local transformations of weakly
non-Gaussian fields that Gaussianize the full multivariate distribution at a
given order in perturbation theory. Our approach does not require a model of
the fields themselves and takes as input only the first few polyspectra, which
could be modelled or measured from simulations or data, making our method
particularly suited to observables lacking a robust perturbative description
such as the weak-lensing shear. We apply our method to simulated density
fields, finding a significantly reduced bispectrum and an enhanced correlation
with the initial field. We demonstrate that our method reconstructs a large
proportion of the linear baryon acoustic oscillations, improving the
information content over the raw field by 35%. We apply the transform to toy
21cm intensity maps, showing that our method still performs well in the
presence of complications such as redshift-space distortions, beam smoothing,
pixel noise, and foreground subtraction. We discuss how this method might
provide a route to constructing a perturbative model of the fully non-Gaussian
multivariate likelihood function.
