Published Paper Details:

Joint cosmological analysis to constrain a time-varying dark energy equation of state using cosmic microwave background (CMB) anisotropy data and galaxy clustering observables from large-scale structure surveys. We extend the standard LambdaCDM model by adopting the Chevallier-Polarski-Linder (CPL) parameterization for the dark energy equation of state, w(z) = w0 + wa z/(1+z), and study its impact on both the background expansion H(z) and the linear growth of matter perturbations. The CMB temperature and polarization spectra, together with CMB lensing, tightly constrain early-universe parameters and the distance to last scattering, while baryon acoustic oscillation (BAO) and redshift-space distortion (RSD) measurements constrain late-time geometry and growth through distance indicators and f sigma8(z). We build a consistent joint likelihood using Planck 2018 TT,TE,EE plus lowE and lensing, combined with BOSS DR12 consensus BAO+RSD constraints at z_eff = 0.38, 0.51, and 0.61. Posterior distributions are sampled using Markov Chain Monte Carlo, and we quantify improvements in constraints on (w0, wa) when adding low-redshift information to the CMB. Model comparison with LambdaCDM is reported using information criteria, and robustness is assessed under alternative assumptions on priors, scale cuts, and neutrino mass treatment. This work provides a complete observationally anchored framework for testing dark energy evolution with current precision cosmology data.