Extracting $H_{0}$ and $r_{d}$ in Pacif Parametrization Models through Late-Time Dataset

This study examines five models derived from the Pacif parametrization scheme of the Hubble parameter ($H$), yielding various linear to quintic forms of the deceleration parameter (DP). Our goal is to explore the impact of these DP variations on late-time evolution and their potential to alleviate cosmological tensions. To enhance model constraints, we introduce non-diagonal elements into the covariance matrix to better capture statistical properties by simulating data point correlations. We also test the sensitivity of $H_{0}$ and $r_{d}$ to the Pacif parametrization scheme, treating the sound horizon $r_{d}$ as a free parameter to avoid imposing a CMB prior. This allows late-time data to constrain $r_{d}$ alongside other cosmological parameters, incorporating recent Baryon Acoustic Oscillations (BAO) measurements and Hubble data from Cosmic Chronometers Methods, Type Ia Supernovae (SNIa), Gamma-Ray Bursts (GRBs), and Quasars over a redshift range of \(0.106 < z < 2.33\). Our analysis provides optimal fit values for $H_{0}$ and $r_{d}$, showing notable consistency with Planck CMB data. By using the Akaike information criterion, we analyze the models and conclude that all models have good agreement with the most recent observations.
Comment: 15 pages, 4 figures