The Pantheon Sample Analysis of Cosmological Constraints under New Models

In this paper, the cosmological parameters are determined by applying six cosmological models to fit the magnitude-redshift relation of the Pantheon Sample consisting of 1048 Type Ia supernovae (SNe Ia) in the range of $0.01 < z < 2.26$. Apart from the well-known flat $\Lambda$CDM model as well as other models that have been broadly studied, this paper includes two new models, the $ow$CDM model and the $ow_{0}w_{a}$CDM model, to fully evaluate the correlations between the cosmological parameters by performing the MCMC algorithm and to explore the geometry and mass content of the Universe. Combining the measurements of the baryon acoustic oscillation (BAO) and the cosmic microwave background (CMB) with the SNe Ia constraints, the matter density parameter $\Omega_\mathrm{M} = 0.328^{+0.018}_{-0.026}$, the curvature of space parameter $\Omega_{k} = 0.0045^{+0.0666}_{-0.0741}$, and the dark energy equation of state parameter $w = -1.120^{+0.143}_{-0.185}$ are measured for the $ow$CDM model. When it comes to the $ow_{0}w_{a}$CDM model, if the parameter $w$ is allowed to evolve with the redshift as $w = w_{0} + w_{a}\left(1-a\right)$, the cosmological parameters are found to be $\Omega_\mathrm{M} = 0.344^{+0.018}_{-0.027}$, $\Omega_{k} = 0.0027^{+0.0665}_{-0.0716}$, $w_{0} = -0.739^{+0.336}_{-0.378}$, and $w_{a} = -0.812^{+0.750}_{-0.678}$. The $ow$CDM model and the $ow_{0}w_{a}$CDM model are able to fit the Pantheon Sample consistently well with $\chi_{\nu}^{2} = 0.994$ and $\chi_{\nu}^{2} = 1.008$, but the parameters $w_{0}$ and $w_{a}$ are not well constrained in both models. Meanwhile, the flat $\Lambda$CDM model is found to fit poorly for $z > 0.5$ high-redshift SNe Ia data with $\chi_{\nu}^{2} = 0.792$ compared to the $w_{0}w_{a}$CDM model with $\chi_{\nu}^{2} = 0.971$ and the $ow_{0}w_{a}$CDM model with $\chi_{\nu}^{2} = 0.824$.