Quantification of High-dimensional Non-Gaussianities and Its Implication to Fisher Analysis in Cosmology

Area of Science:

• Cosmology
• Statistical physics
• Astrophysics

Background:

• The power spectrum alone is insufficient for characterizing non-Gaussian cosmological density fields.
• Various statistics are proposed to improve information extraction from non-Gaussian fields.
• Fisher matrix formalism commonly assumes multivariate Gaussian distributions for statistics, potentially leading to inaccurate cosmological parameter constraints.

Purpose of the Study:

• To identify and remove non-Gaussian components from cosmological statistics.
• To assess the impact of non-Gaussianity on Fisher matrix calculations for cosmological parameters.
• To provide a robust method for evaluating the reliability of Fisher matrix analyses.

Main Methods:

• Utilized two statistical tests to detect non-Gaussianities in power spectrum, bispectrum, marked power spectrum, and wavelet scattering transform (WST).
• Applied Gaussianization techniques to remove non-Gaussian components from these statistics.
• Performed Fisher matrix calculations on Gaussianized statistics using Quijote simulations.

Main Results:

• Identified non-Gaussianities in various cosmological statistics.
• Demonstrated that removing non-Gaussian components can alter parameter constraints by up to a factor of ~2.
• Showcased how non-Gaussian statistics can yield artificially tight bounds in Fisher matrix analyses.

Conclusions:

• Non-Gaussianity tests are crucial for validating Fisher matrix calculations in cosmology.
• Gaussianized statistics provide more robust constraints on cosmological parameters.
• The developed methods and released code enhance the reliability of cosmological parameter estimation.