Probing Cosmic Background Dynamics with a Cosmological-model-independent Method

The Hubble constant $H_0$ tension has emerged as the most serious crisis in modern cosmology, potentially indicating that the $\Lambda$CDM model may not describe our universe accurately. In this paper, we establish a new, cosmological-model-independent method to study the cosmic background dynamics. Using the latest Pantheon+ Type Ia supernova (SN Ia) sample and the model-independent SN Ia sample (P+1690), we derive values for the luminosity distance, the Hubble parameter, and the deceleration parameter at five different redshift points ranging from 0.12 to 0.52. Our analysis shows that results obtained from the Pantheon+ sample align with the predictions of the $\Lambda$CDM model within 2$\sigma$ confidence level (CL), while those obtained from the P+1690 sample exhibit deviations of about $2\sim3\sigma$ CL. Furthermore, we explore the equation of state (EoS) of dark energy and find that while the EoS values from the Pantheon+ sample remain consistent with $-1$ within 2$\sigma$ CL, the P+1690 sample does not conform to this standard. These findings remain unchanged after the inclusion of the Hubble parameter measurements in our analysis. Our results indicate that the $\Lambda$CDM model remains compatible with the Pantheon+ SN Ia and the Hubble parameter measurements at 2$\sigma$ CL.