Transitioning late-time cosmology with the Hubble parameterization

We investigate a late-time cosmological model for a homogeneous and isotropic space-time in the Rastall theory. We explore the observational constraints on the Hubble parameter by using the latest cosmological datasets such as cosmic microwave background radiation (Planck), baryon acoustic oscillations (DESI) and Type Ia Supernovae (Union 3.0). As a result, we explicitly demonstrate that the specific redshift transition occurs, namely, there happens a phase shift in the evolution of the universe from the initial deceleration era to the current accelerating phase of the cosmological scenario. Furthermore, we show that with the latest dataset of DESI-BAO clubbed with CC, CMB, and Union 3.0, the current value of the Hubble parameter is estimated as $H_0=66.945\pm 1.094$, which can be compatible with the available observations.