Testing Non-Coincident $f(Q)$-gravity with DESI DR2 BAO and GRBs

We consider the $f\left( Q \right) $-theory for the description of dark energy with a non-trivial connection defined in the non-coincident gauge. The resulting field equations form a two-scalar-field, quintom-like gravitational model. For the power-law model $f\left( Q \right) \simeq Q^{\frac{n}{n-1}}$, we construct an analytic expression for the dynamical evolution of dark energy, which depends on the parameter $n$. We constrain this dark energy model using the the baryon acoustic oscillations from DESI DR2, and gamma-ray bursts. The cosmological data provides $n \simeq0.33 $. The $f\left( Q \right) $-model challenges the $\Lambda$CDM by providing a smaller value for $\chi_{\min}^{2}$, while there is weak evidence in favor of the $f\left( Q \right) $-theory.