An optimal basis system for cosmology: data analysis and new parameterisation

TL;DR

This paper introduces an optimal basis system for decomposing cosmological observables, enabling efficient model comparison, degeneracy analysis, and reconstruction of the Hubble rate from observational data.

Contribution

It presents a novel, optimizable basis system for cosmological data analysis that simplifies model comparison and reconstruction tasks.

Findings

Efficient comparison of different cosmological models.

Ability to reconstruct the Hubble rate from data.

Validation on mock and real supernova data.

Abstract

We define an optimal basis system into which cosmological observables can be decomposed. The basis system can be optimised for a specific cosmological model or for an ensemble of models, even if based on drastically different physical assumptions. The projection coefficients derived from this basis system, the so-called features, provide a common parameterisation for studying and comparing different cosmological models independently of their physical construction. They can be used to directly compare different cosmologies and study their degeneracies in terms of a simple metric separation. This is a very convenient approach, since only very few realisations have to be computed, in contrast to Markov-Chain Monte Carlo methods. Finally, the proposed basis system can be applied to reconstruct the Hubble expansion rate from supernova luminosity distance data with the advantage of being sensitive to possible unexpected features in the data set. We test the method both on mock catalogues and on the SuperNova Legacy Survey data set.