On the Gaussian Assumption in the Estimation of Parameters for Dark Energy Models

TL;DR

This paper critically examines the common Gaussian assumption in supernova data analysis for dark energy models, finding that a t-distribution better describes the data, which impacts parameter estimation accuracy.

Contribution

It provides a rigorous statistical assessment of the Gaussianity assumption in supernova data and introduces a more accurate t-distribution model for parameter estimation in dark energy cosmology.

Findings

Gaussianity assumption is invalid for supernova data

Redshift distribution is better modeled by a t-distribution

Parameter estimates vary significantly when using the t-distribution

Abstract

Type Ia supernovae have provided fundamental observational data in the discovery of the late acceleration of the expansion of the Universe in cosmology. However, this analysis has relied on the assumption of a Gaussian distribution for the data, a hypothesis that can be challenged with the increasing volume and precision of available supernova data. In this work, we rigorously assess this Gaussianity hypothesis and analyze its impact on parameter estimation for dark energy cosmological models. We utilize the Pantheon+ dataset and perform a comprehensive statistical, analysis including the Lilliefors and Jarque-Bera tests, to assess the normality of both the data and model residuals. We find that the Gaussianity assumption is untenable and that the redshift distribution is more accurately described by a t-distribution, as indicated by the Kolmogorov Smirnov test. Parameters are estimated for a model incorporating a nonlinear cosmological interaction for the dark sector. The free parameters are estimated using multiple methods, and bootstrap confidence intervals are constructed for them.