Observational Constraints on Noncoincident $f(Q)$-Gravity with Matter-Gravity Coupling

We investigate $f\left( Q\right)$-gravity with a matter-gravity coupling as a geometric dark energy candidate for the description of the late-time cosmic acceleration within a spatially flat Friedmann--Lema\^{\i}tre-Robertson-Walker geometry. We select a noncoincident connection that naturally follows from the general framework of cosmological models with nonzero spatial curvature. We present observational constraints for the simplest $f\left( Q\right) =f_{0}Q^{n}$ model using data from Supernovae, Baryon Acoustic Oscillations and Cosmic Chronometers. For different data combinations we found consistent constraints, with a best-fit value for the power-law index $n\simeq2$. A comparison with the $\Lambda$CDM model shows that the $f\left( Q\right)$-gravity leads to larger values for the likelihood, while Akaike's Information Criterion suggests statistical equivalence between the two models for most data combinations.