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The Hubble constant $H_0$ tension has emerged as the most serious crisis inmodern cosmology, potentially indicating that the $\Lambda$CDM model may notdescribe 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 themodel-independent SN Ia sample (P+1690), we derive values for the luminositydistance, the Hubble parameter, and the deceleration parameter at fivedifferent redshift points ranging from 0.12 to 0.52. Our analysis shows thatresults obtained from the Pantheon+ sample align with the predictions of the$\Lambda$CDM model within 2$\sigma$ confidence level (CL), while those obtainedfrom the P+1690 sample exhibit deviations of about $2\sim3\sigma$ CL.Furthermore, we explore the equation of state (EoS) of dark energy and findthat 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. Thesefindings remain unchanged after the inclusion of the Hubble parametermeasurements in our analysis. Our results indicate that the $\Lambda$CDM modelremains compatible with the Pantheon+ SN Ia and the Hubble parametermeasurements at 2$\sigma$ CL.

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