Bayesian and Machine-Learning Analyses of Nonminimal $f(Q)$ Gravity and $H_0$ Tension

TL;DR

This paper explores nonminimal $f(Q)$ gravity within the metric-affine formalism, combining statistical and machine learning analyses to assess its potential in alleviating the $H_0$ tension and its viability for late-time cosmology.

Contribution

It introduces a representative $f(Q)$ model in the symmetric teleparallel framework and employs both statistical and machine learning methods to evaluate its cosmological implications.

Findings

Partial alleviation of the $H_0$ tension was observed.

$f(Q)$ gravity shows promise as a flexible late-time cosmology framework.

Machine learning methods support the robustness of the statistical results.

Abstract

In this study, the cosmological implications of nonminimally coupled $f(Q)$ gravity are examined within the metric-affine formalism, in which the nonmetricity scalar $Q$ couples directly to the matter Lagrangian. Within the symmetric teleparallel framework, a representative $f(Q)$ model is constructed, and the corresponding background cosmological equations are derived. The analysis aims to test whether this geometric formulation yields more consistent realizations of nonminimal matter-geometry couplings. A comprehensive statistical MCMC analysis is performed using cosmic chronometers, DESI BAO DR2, and Type Ia supernovae from the Pantheon+, DESY5, and Union3 samples. To complement the statistical study, we employ machine learning methods, such as linear regression, support vector regression (SVR), and random forest algorithms, to evaluate the predictive performance and robustness of the data. The results indicate that a partial alleviation of the $H_0$ tension can be achieved for a broad range of parameter choices. Nonetheless, $f(Q)$ gravity emerges as a promising and flexible framework for late-time cosmology, motivating further exploration of extended models consistent with all observations.