Early and Late Observational Tension: Dark Energy Parametrizations in Horava-Lifshitz Gravity via Baryon Acoustic Oscillations

Abstract We investigate late-time cosmic expansion within the Horava Lifshitz gravity framework using Barboza Alcaniz (BA) and Jassal Bagla Padmanabhan Parametrizations (JBP) as alternatives to general relativity. Anisotropic scaling is introduced at ultraviolet scales. Our aim is to constrain each cosmological parameter using the crucial Baryon Acoustic Oscillation (BAO) scale, specifically the sound horizon ( r d ), by treating ( r d ) as a free parameter. We employ 30 Hubble parameter measurements ( H ( z )) from cosmic chronometers, along with Type Ia Supernovae, Gamma-Ray Bursts, Quasars, and 24 uncorrelated BAO measurements spanning z = 0.106 to z = 2.33. The analysis includes the 2022 Hubble constant measurement by Riess (R22) as an additional prior and aims to minimize errors by simulating random correlations in the covariance matrix. In both the BA and JBP frameworks, utilizing the full dataset yields sound horizon results of r d = 146.5399 ± 2.4519 Mpc and r d = 146.4533 ± 2.4519 Mpc, respectively. When incorporating R22 results, the sound horizon values become r d = 143.4721 ± 1.8324 Mpc and r d = 142.9826 ± 1.9084 Mpc. These findings reveal a discrepancy between early and late observations, echoing the H 0 tension. Notably, excluding R22 aligns r d with Planck and SDSS results. Model predictions are evaluated against Hubble Measurements and the ΛCDM Paradigm. A comparative study between BA and JBP Models using the Cosmography test shows both models fitting seamlessly within the phantom region. Statistical analysis suggests neither model can be ruled out based on the latest observational measurements.