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

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 a priori assumptions on the cosmological model. To this purpose, we adopt a method based on rational Padé 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)=α+βQn. Finally, possible deviations from the standard ΛCDM model are discussed.