Perturbative Gaussianizing transforms for cosmological fields

TL;DR

This paper introduces a perturbative Gaussianizing transform for cosmological fields that enhances information extraction by reducing non-Gaussian features, applicable to various observables including weak lensing and 21cm maps.

Contribution

It presents a novel, model-independent method to Gaussianize non-Gaussian cosmological fields using only low-order polyspectra, improving parameter constraints.

Findings

Reduces bispectrum significantly in simulated density fields.

Reconstructs a large portion of linear baryon acoustic oscillations.

Performs well on toy 21cm maps despite observational complications.

Abstract

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.