Optimising Gaussian processes for reconstructing dark energy dynamics from supernovae

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.