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.
