Towards a model-independent reconstruction approach for late-time Hubble data

TL;DR

This paper develops a model-independent method using Gaussian processes with advanced kernel selection techniques to reconstruct late-time cosmological data, identifying the most suitable kernels for cosmic chronometers and supernovae data.

Contribution

It introduces two novel methods for kernel selection in Gaussian processes and applies them to cosmological data, improving nonparametric reconstruction accuracy.

Findings

The Matérn (ν=5/2) kernel performs best for both data sets.

A hybrid Radial Basis Function and Matérn kernel provides the best fit.

Kernel choice remains an open problem requiring further research.

Abstract

Gaussian processes offers a convenient way to perform nonparametric reconstructions of observational data assuming only a kernel which describes the covariance between neighbouring points in a data set. We approach the ambiguity in the choice of kernel in Gaussian processes with two methods -- (a) approximate Bayesian computation with sequential Monte Carlo sampling and (b) genetic algorithm -- and use the overall resulting method to reconstruct the cosmic chronometers and supernovae type Ia data sets. The results have shown that the Mat\'{e}rn$\left( \nu = 5/2 \right)$ kernel emerges on top of the two-hyperparameter family of kernels for both cosmological data sets. On the other hand, we use the genetic algorithm in order to select a most naturally-fit kernel among a competitive pool made up of a ten-hyperparameters class of kernels. Imposing a Bayesian information criterion-inspired measure of the fitness, the results have shown that a hybrid of the Radial Basis Function and the Mat\'{e}rn$\left( \nu = 5/2 \right)$ kernel best represented both data sets. The kernel selection problem is not totally closed and may benefit from further analysis using other strategies to resolve an optimal kernel for a particular data set.