Model-independent test of the running Hubble constant from the Type Ia supernovae and the Hubble parameter data

Abstract

In this study, we model-independently investigate the behavior of running Hubble constant, characterized by the fit function $H_{\rm 0}(z)=\tilde{H_{\rm {0}}}/(1+z)^{\alpha }$, where α represents the evolutionary parameter and ${\tilde{H_{\rm {0}}}}$ corresponds to the current value of Hubble constant. Our analysis utilizes the expansion rate E(z) data points measured from the Pantheon+MCT compilation of Type Ia supernovae data, the measurements of H0 obtained by Riess et al., and the Hubble parameter H(z) data obtained from the differential ages of passive galaxies (known as cosmic chronometers (CC) method) and from the Baryon Acoustic Oscillation (BAO) in the radial direction of galaxy clustering. To resolve the redshift mismatch problem between the E(z) and H(z) datasets, we adopt the Hubble parameter data obtained via CC or BAO along with the measurements of H0 obtained by Riess et al. to reconstruct the H(z) function using the Gaussian process. Our constraint yields α values of 0.125 ± 0.063 or 0.095 ± 0.052 when combining six pairs of the E(z) data and the reconstructed H(z) points via CC or BAO. These findings reveal the Hubble constant may evolve with redshift, exhibiting a slowly decreasing trend, with α coefficients consistent with zero only at 2.0 or 1.8σ. Therefore, the running Hubble constant might offer a promising resolution to the Hubble tension, and its reliability should be further tested through high-precision measurement at higher redshifts, such as the upcoming Gamma-Ray Bursts, and quasars.