Constraints on ΛCDM and XCDM Cosmological Models Using Pantheon+ SN Type Ia, Hubble parameter, and BAO Datasets

A comprehensive statistical analysis of cosmological parameters is presented, utilizing Supernova H₀ for the Equation of State (SH0ES) calibrated redshift and distance modulus Pantheon+ Type Ia supernovae data, with statistical and systematic uncertainty covariance matrix, Hubble parameter data, and Baryon Acoustic Oscillation (BAO) distance measurements data. This study explores both flat and non-flat ΛCDM and XCDM models solving the Friedmann and continuity equations in differential equation forms using the fourth-order Runge-Kutta (RK45) numerical method and performing a joint Bayesian model-dependent analysis. The Markov Chain Monte Carlo (MCMC) technique is implemented through the EMCEE Python module to sample the parameter space while computing chi-square statistics, log-likelihood functions, and model selection criteria such as the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC). By analyzing different combinations of datasets, the constraints on the Hubble parameter (H₀), matter density parameter (Ω_m), spatial curvature density parameter (Ω_k), and equation of state of dark energy (w₀) are examined. The Pantheon+ dataset yields H₀= 72.85 ± 0.19, Ω_m0 = 0.358 ± 0.01, H(z) + BAO dataset yields H₀= 68.50 ± 0.90 and Ω_m0= 0.292 ± 0.09 , and full joint dataset yields H₀ = 70.58 ± 0.14, Ω_m0 = 0.364 ± 0.01. These analysis suggest a significantly flat curvature and highlight the impact of the dataset selection on the constraints of the cosmological parameters.