Cosmological constraints in covariant $f(Q)$ gravity with different connections

Recently it has been shown that the cosmological dynamics of covariant $f(Q)$ gravity depend on different affine connections. In this paper, two specific $f(Q)$ models are investigated with SNe+CC+BAO+QSO observational data, and the spatial curvature of the universe is studied in covariant $f(Q)$ gravity. It is found that the parameters $\mathcal{X}_0$ and $\mathcal{X}'_0$ characterizing affine connections significantly affect the behavior of the effective equation of state $w_Q$ and may drive it across the phantom divide line. These results imply some inertial effects of the universe change the cosmic dynamics. However based on the Bayesian evidence, the zero inertial effect is more favored in the flat universe. Moreover, a closed universe is favored not only in the $\Lambda$CDM model but also in covariant $f(Q)$ gravity. The $f(Q)$ models have less support evidence than the $\Lambda$CDM model in the non-flat universe.