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

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 Locally weighted Scatterplot Smoothing together with Simulation and extrapolation method (LOESS-Simex or LS). 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 σ GP−min = 1.1, while the situation for LS is totally different with a minimum of σ LS−min = 50.8. Moreover, some of these characteristics can be alliviate at low z, where LS presents less underestimation in comparison to GP.

f(T, B) Cosmography for High Redshifts

“…It would also be advantageous to consider other approaches to constraining the evolution of the cosmographic parameters such as the non-parametric ones proposed in Refs. [75][76][77].…”

Teleparallel Gravity: From Theory to Cosmology

“…Thus, given a set of Gaussian distributed data points, GP provide an iterative process by which to produce the most likely underlying continuous function that describes the data together with its associated confidence bounds without assuming a prescribed form of the function [951]. In the current era of precision cosmology with multiple state-of-the-art surveys, GP has been exhaustively applied in cosmology [960,951,1092,233,1048,1105,240,773,528,1095,43,700,706,1093,428,695], particularly to infer the late-time dynamics of the Universe.…”

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

“…While GP is model-independent in the cosmological context, it does rely on a some statistical background in order to determine an appropriate kernel choice. In the Hubble diagram context, this can lead to slightly different values for the H 0 parameter as shown in previous studies as well [19,[35][36][37]. To visualize this issue better, consider the following kernels (more details in section 2): radial basis function (RBF), Rational quadratic (RQ), Matérn with index ν = x/2 (Mx2).…”

“…In ref. [37] GP was contrasted with Locally weighted Scatterplot Smoothing together with Simulation and extrapolation method (LOESS-Simex) using a number of approaches to characterizing the performance of each reconstruction approach. Another interesting approach to the kernel tension problem is ref.…”