Non-Linear Cosmology Dynamics

Assuming the data has a Gaussian distribution (i.e. is distributed in a "normal" probability curve) is often reasonable, since this is what happens when data comes from independent simple percentage probability events. And, it is a convenient assumption when it works, because mathematically it is much easier to work with Gaussian distributions than most other probability distributions. But, sometimes reality is more complicated than that and this assumption isn't reasonable. 

The supernova data used to characterize dark energy phenomena isn't Gaussian. 

Trivially, this means that statistical uncertainty estimates based upon Gaussian distributions overestimate the statistical significance of observations in the fat tailed t-distribution. 

Non-trivially, this means that the underlying physics of dark matter phenomena are more mathematically complex than something like Newtonian gravity (often assumed for astronomy purposes as a reasonable approximation of general relativity) or a simple cosmological constant. Simple cosmology models don't match the data. 

This paper estimates dark energy parameters for more complex dark energy models that can fit the data.

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.

Fabiola Arevalo, Luis Firinguetti, Marcos Peña, "On the Gaussian Assumption in the Estimation of Parameters for Dark Energy Models" arXiv:2507.05468 (July 7, 2025).