Performance of Non-Parametric Reconstruction Techniques in the Late-Time Universe

TL;DR

This paper compares Gaussian processes and LOESS-Simex non-parametric methods for reconstructing cosmological data, highlighting their differences in uncertainty estimation and implications for the Hubble tension.

Contribution

It provides a detailed comparison of GP and LS methods applied to cosmological data, emphasizing their effectiveness and uncertainties without relying on specific cosmological models.

Findings

GP yields smaller uncertainties than LS for data reconstruction.

LS performs better at low redshift with less underestimation.

Both methods successfully reconstruct data with high precision.

Abstract

In the context of a Hubble tension problem that is growing in its statistical significance, we reconsider the effectiveness of non-parametric reconstruction techniques which are independent of prescriptive cosmological models. By taking cosmic chronometers, Type Ia Supernovae and baryonic acoustic oscillation data, we compare and contrast two important reconstruction approaches, namely Gaussian processes (GP) and the \textbf{Lo}cally w\textbf{e}ighted \textbf{S}catterplot \textbf{S}moothing together with \textbf{Sim}ulation and \textbf{ex}trapolation method (LOESS-Simex or LS). In the context of these methods, besides not requiring a cosmological model, they also do not require physical parameters in their approach to their reconstruction of data (but they do depend on statistical hyperparameters). We firstly show how both GP and LOESS-Simex can be used to successively reconstruct various data sets to a high level of precision. We then directly compare both approaches in a quantitative manner by considering several factors, such as how well the reconstructions approximate the data sets themselves to how their respective uncertainties evolve. In light of the puzzling Hubble tension, it is important to consider how the uncertain regions evolve over redshift and the methods compare for estimating cosmological parameters at current times. For cosmic chronometers and baryonic acoustic oscillation compiled data sets, we find that GP generically produce smaller variances for the reconstructed data with a minimum value of $\sigma_{\rm GP-min} = 1.1$, while the situation for LS is totally different with a minimum of $\sigma_{\rm LS-min} = 50.8$. Moreover, some of these characteristics can be alleviate at low $z$, where LS presents less underestimation in comparison to GP.