Crossing Statistic: Bayesian interpretation, model selection and resolving dark energy parametrization problem

TL;DR

The paper introduces a Bayesian approach using Crossing functions and hyper-parameters for model selection in cosmology, enabling model falsification without assuming specific parametrizations or priors, and demonstrating robustness to data uncertainties.

Contribution

It presents a novel Bayesian interpretation of Crossing Statistics that simplifies model selection and falsification in cosmology without relying on priors or specific parametrizations.

Findings

Method effectively falsifies cosmological models.

Insensitive to data dispersion and uncertainties.

Does not require priors on universe models.

Abstract

By introducing Crossing functions and hyper-parameters I show that the Bayesian interpretation of the Crossing Statistics [1] can be used trivially for the purpose of model selection among cosmological models. In this approach to falsify a cosmological model there is no need to compare it with other models or assume any particular form of parametrization for the cosmological quantities like luminosity distance, Hubble parameter or equation of state of dark energy. Instead, hyper-parameters of Crossing functions perform as discriminators between correct and wrong models. Using this approach one can falsify any assumed cosmological model without putting priors on the underlying actual model of the universe and its parameters, hence the issue of dark energy parametrization is resolved. It will be also shown that the sensitivity of the method to the intrinsic dispersion of the data is small that is another important characteristic of the method in testing cosmological models dealing with data with high uncertainties.