Model-independent reconstruction of $f(Q)$ non-metric gravity

TL;DR

This paper introduces a model-independent method to reconstruct the $f(Q)$ non-metric gravity action using rational Padé approximations, enabling analysis of dark energy effects without assuming specific cosmological models.

Contribution

It presents a novel reconstruction technique for $f(Q)$ gravity based on rational Padé approximations, improving stability at high redshifts and avoiding prior model assumptions.

Findings

Reconstructed $f(Q)$ as $ ext{alpha} + ext{beta} Q^{n}$ best fits accelerated expansion.

Method effectively handles convergence issues at high redshifts.

Discussed deviations from $ ext{Lambda}$CDM model.

Abstract

We consider gravity mediated by non-metricity, with vanishing curvature and torsion. The gravitational action, including an arbitrary function of the non-metric scalar, is investigated in view of characterizing the dark energy effects. In particular, we present a method to reconstruct the $f(Q)$ action without resorting to \emph{a priori} assumptions on the cosmological model. To this purpose, we adopt a method based on rational Pad\'e approximations, which provides a stable behaviour of the cosmographic series at high redshifts, alleviating the convergence issues proper of the standard approach. We thus describe how to reconstruct $f(Q)$ through a numerical inversion procedure based on the current observational bounds on cosmographic parameters. Our analysis suggests that the best approximation for describing the accelerated expansion of the universe is represented by a scenario with $f(Q)=\alpha+\beta Q^{n}$. Finally, possible deviations from the standard $\Lambda$CDM model are discussed.