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

Abstract

This study examines accelerated cosmic expansion using the Viscous Modified Chaplygin Gas (VMMG) and Generalized Cosmic Chaplygin Gas (GCCM) within Horava-Lifshitz gravity. Our aim is to constrain essential cosmological parameters, such as the Hubble Parameter ($H_{0}$) and Sound Horizon ($r_{d}$). We utilize late-time datasets: 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, along with the latest determination of the Hubble constant (R22). Treating $r_{d}$ as a free parameter offers several advantages, including mitigating bias, enhancing precision, and improving compatibility with various datasets. By introducing random correlations in the covariance matrix during simulation, errors are effectively reduced. Our estimated values of the Hubble constant ($H_0$) and $r_{d}$ consistently align with measurements from both the Planck and SDSS experiments. Cosmographic tests provide valuable insights into the dynamics of various cosmological models, enriching our understanding of cosmic evolution. Statefinder diagnostics offer deeper insights into cosmic expansion dynamics, aiding in distinguishing between cosmological frameworks. Furthermore, the $o_{m}$ diagnostic test reveals that at late times, VMMG falls into the phantom region, while GCCM falls into the quintessence region. The Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) support all models, indicating plausible explanations. Notably, the $Λ$CDM model emerges with the lowest AIC score, suggesting its relatively superior fit. Validation via the reduced $χ_{\text{red}}^{2}$ statistic confirms satisfactory fits across all models, reinforcing their credibility.