Investigating the relationship between cosmic curvature and dark energy models with the latest supernova sample

We investigate the relationship between the cosmic curvature and the model of dark energy (hereafter DE) with the recent Type Ia supernovae (hereafter SNe Ia) data, i.e., the Pantheon sample including 1048 SNe Ia with $0.01 < z < 2.3$. We obtain the measurements of the dimensionless spatial curvature density today, i.e., $\Omega_{k0} = -0.062^{+0.189}_{-0.169}, -0.004^{+0.228}_{-0.134}, 0.127^{+0.280}_{-0.276}$ and $0.422^{+0.213}_{-0.338}$ at 68\% confidence level (CL), respectively, in the scenarios of $\Lambda$CDM, $\phi$CDM (i.e., scalar field dark energy), $\omega$CDM and $\omega_0\omega_a$CDM models. In the scenario of $\Lambda$CDM model, a closed universe is preferred by the Pantheon sample, which is consistent with that from the Planck CMB spectra. However, the uncertainty of $\Omega_{k0}$ from the Pantheon SNe sample is about 8 times larger than that from the Planck data, so the former one supports a closed universe at a much lower CL than that from the latter one. An open unverse is supported by the Pantheon sample at $\sim$32\% and $\sim$78\% CLs, respectively, in the $\omega$CDM and $\omega_0\omega_a$CDM models. Among these models, the $\phi$CDM model is the one which supports the flat universe most strongly. It shows that $\Omega_{k0}$ is significantly dependent on the adopted model of dark energy, and there is a negative correlation between $\Omega_{k0}$ and the equation of state of DE.