Optimising Gaussian processes for reconstructing dark energy dynamics from supernovae

TL;DR

This paper explores how to optimize Gaussian processes for reconstructing dark energy dynamics from supernovae data, emphasizing the importance of covariance function choice and introducing a method to assess deviations from models.

Contribution

It demonstrates the impact of covariance function selection on Gaussian process reconstructions and proposes a new method to quantify deviations from these reconstructions.

Findings

Choice of covariance function significantly influences reconstruction results.

A reliable covariance function for supernovae data is identified.

A novel method to measure deviations from Gaussian process reconstructions is introduced.

Abstract

Gaussian processes are a fully Bayesian smoothing technique that allows for the reconstruction of a function and its derivatives directly from observational data, without assuming a specific model or choosing a parameterization. This is ideal for constraining dark energy because physical models are generally phenomenological and poorly motivated. Model-independent constraints on dark energy are an especially important alternative to parameterized models, as the priors involved have an entirely different source so can be used to check constraints formulated from models or parameterizations. A critical prior for Gaussian process reconstruction lies in the choice of covariance function. We show how the choice of covariance function affects the result of the reconstruction, and present a choice which leads to reliable results for present day supernovae data. We also introduce a method to quantify deviations of a model from the Gaussian process reconstructions.