Quantum gravity

Effective action

Physics

Gravitation

Metric (unit)

Metric expansion of space

Mathematics

Mathematical physics

Scalar curvature

Epistemology

f(R) gravity

Philosophy

Economics

Dark energy

Curvature

Operations management

Geometry

Cosmology

Lambda

Theoretical physics

Quantum mechanics

A priori and a posteriori

Classical mechanics

Quantum

Physics Letters B

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.

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