Bayesian analysis of viscous modified cosmic Chaplygin gas in FRW universe with a cosmological constant

In this work, we have studied the viscous Modified Cosmic Chaplygin Gas (MCCG) in the appearance of a cosmological constant within the FRW model of the universe. We assume that the bulk viscosity \(\xi\) and the cosmological constant \(\Lambda\) are linear combinations of two terms: one constant and the other dependent on the dark energy density \(\rho\) . In this work, we solve the resulting non-linear differential equations both analytically and numerically, obtaining the time evolution of the dark energy density. Using detailed calculations within the FRW framework, we derive an H ( z ) model and constrain its parameters through Bayesian statistical analysis, specifically via the Markov Chain Monte Carlo (MCMC) method, employing observational Hubble data (OHD), the Pantheon Plus, RSD, Union3 and DESI BAO datasets. Additionally, we have employed combined datasets such as CC+PP , CC+PP+RSD , CC+PP+RSD+DESI and CC+PP+RSD+DESI+Union3 .