Extracting H₀ and rd in Pacif Parametrization Models through Late-Time Data with Covariance Matrix Simulation

The study analyzes five models derived from the Pacif parametrization scheme, a generalized form of the Hubble parameter (H), yielding various forms of the deceleration parameter (DP) that vary linearly, quadratically, cubically, quartically, and quintically. We aim to explore the impact of these DP variations on late-time evolution and their potential to alleviate cosmological tensions. Additionally, we enhance model constraints by introducing non-diagonal elements into the covariance matrix, thereby simulating correlations between data points and better capturing the true statistical properties of the dataset. Furthermore, our objective is to test the sensitivity of H₀ and rd to the Pacif parametrization scheme. To avoid imposing a prior from CMB, we treat the sound horizon rd as a free parameter, allowing the late-time data itself to constrain the value of rd along with other cosmological parameters. This is achieved by incorporating the most recent measurements, such as Baryon Acoustic Oscillations (BAO) from the latest galaxy surveys. The considered redshift range spans from (0.106 < z < 2.33), encompassing Hubble measurements obtained through Cosmic Chronometers Methods, Type Ia Supernovae (SNIa), Gamma-Ray Bursts (GRBs), and Quasars (Q). Additionally, an extra constraint is introduced by integrating the latest Hubble constant measurement from Riess in 2022. Our analysis yields optimal fit values for the Hubble parameter H₀ and sound horizon rd. The results highlight a notable consistency between the values derived from the Pacif parametrization models and those obtained from Planck CMB data. Finally, we employ the Akaike information criterion approach to compare the three models, revealing that none of them can be discounted based on the latest observational measurements.