Evaluating extensions to LCDM: an application of Bayesian model averaging and selection

We present a powerful and innovative statistical framework to address key cosmological questions about the universe's fundamental properties, performing Bayesian model averaging (BMA) and model selection. Utilizing this framework, we systematically explore extensions beyond the standard Lambda CDM model, considering a varying curvature density parameter ohm(K), a spectral index n(s) = 1 and a varying n(run), a constant dark energy equation of state (EOS)w(0)CDM and a time-dependent one w(0)w(a)CDM. We also assess cosmological data against a varying effective number of neutrino species N-eff. Our analysis incorporates data from various combinations of cosmic microwave background (CMB) data from the latest Planck PR4 analysis, CMB lensing from Planck 2018, baryonic acoustic oscillations (BAO), and the Bicep-KECK 2018 results. We reinforce the standard Lambda CDM model statistical preference when combining CMB data with CMB lensing, BAO, and Bicep-KECK 2018 data against the K-Lambda CDM model and dn(s)/d ln k-Lambda CDM with a probability > 80%. When evaluating the dark energy EOS, we find that this dataset does not exhibit a strong preference between the standard Lambda CDM model and the constant dark energy EOS model w(0)CDM, with a model posterior probability distribution of approximately approximate to 40% : 60% in favour of w(0)CDM, while the time-varying dark energy EOS model only holds below 1% probability. We find a similar result also when considering the N-eff-Lambda CDM model, with a split probability almost 50%-50% from both our datasets. Overall, our application of BMA reveals that including model uncertainty in these cases does not significantly impact the Hubble tension, showcasing BMA's robustness and utility in cosmological model evaluation.