Constraining Cosmological Parameters with Viscous Modified Chaplygin Gas and Generalized Cosmic Chaplygin Gas Models in Horava-Lifshitz Gravity: Utilizing Late-time Datasets

This study investigates accelerated cosmic expansion using the Viscous Modified Chaplygin Gas (VMMG) and Generalized Cosmic Chaplygin Gas (GCCM) within Horava-Lifshitz gravity. Our primary objective is to constrain essential cosmological parameters, such as the Hubble Parameter (H_0) and Sound Horizon (r_d). We incorporate recent datasets comprising 17 Baryon Acoustic Oscillation observations, 33 Cosmic Chronometer measurements, 40 Type Ia Supernovae data points, 24 quasar Hubble diagram data points, and 162 Gamma Ray Bursts data points. Additionally, we integrate the most recent determination of the Hubble constant (R22). Treating r_d as a free parameter helps alleviate bias, enhance precision, and improve dataset compatibility. By simulating random correlations in the covariance matrix, errors are reduced. The obtained values of (H_0) and (r_d) are consistent with those from Planck and SDSS. Cosmography tests offer insights into the dynamics of both models, aiding our understanding of cosmological evolution. Statefinder diagnostics deepen our understanding of cosmic expansion dynamics and aid in distinguishing between different cosmological models. The o_m Diagnostic test reveals that at late times, VMMG falls in the phantom region and GCCM falls in the phantom quintessence region. The Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) provide support for all models under consideration, indicating that each model offers a plausible explanation. Notably, the ΛCDM model emerges with the lowest AIC score, suggesting its relatively superior fit compared to others. Additionally, validation through the reduced χ_red^2 statistic confirms satisfactory fits across all models, further reinforcing their credibility in explaining the observed data.