Constraining Dark Matter Parameters in the ΛCDM Framework: A Bayesian Comparison of Planck and DES Constraints

Abstract

We present a Bayesian analysis of cosmological parameter constraints from early- and late-universe observations, focusing on the matter density parameter (Ωm ) and the amplitude of matter fluctuations (σ8 ) within the ΛCDM framework. Using data from the Planck 2018 satellite mission and the Dark Energy Survey (DES) Year 3, we compute theoretical predictions for angular and matter power spectra via Boltzmann solvers and perform Markov Chain Monte Carlo (MCMC) sampling using the emcee Python package. Our key contribution is a direct and quantitative comparison of DES and Planck constraints, assessing their consistency using chi-squared analysis and Gaussian tension metrics. We find a statistically significant 6.46σ tension in Ωm and a 2.68σ tension in σ8 between the two datasets. These results provide fresh evidence of persistent discrepancies in cosmological parameter estimates and suggest that simple extensions to the ΛCDM model may be insufficient to fully reconcile early- and late-time observations, motivating the need for more complex theoretical models or refined treatment of systematics.