Evaluating extensions to LCDM: an application of Bayesian model averaging

We employ Bayesian Model Averaging (BMA) as a powerful statistical framework to address key cosmological questions about the universe's fundamental properties. We explore extensions beyond the standard ΛCDM model, considering a varying curvature density parameter Ωₖ, a spectral index nₛ=1 with running dnₛ/dk, a constant dark energy equation of state (EOS) w₀-ΛCDM and a time-dependent one w₀wₐ-ΛCDM. We also test cosmological data against a varying effective number of neutrino species Neff. Data from different combinations of cosmic microwave background (CMB) data from the last Planck PR4 analysis, CMB lensing from Planck 2018, baryonic acoustic oscillations (BAO) and the Bicep-KECK 2018 results, are used. We find that the standard ΛCDM model is favoured when combining CMB data with CMB lensing, BAO and Bicep-KECK 2018 data against k-ΛCDM model Neff-ΛCDM with a probability $> 80%$. When investigating the dark energy EOS, we find that this dataset is not able to express a strong preference between the standard ΛCDM model and the constant dark energy EOS model w₀-ΛCDM, with an approximately split model posterior probability of ≈ 60%:40% in favour of ΛCDM, whereas the time-varying dark energy EOS model is ruled out. Finally, we find that the CMB data alone show a strong preference for a model that includes the running of the spectral index dnₛ/dk, with a probability ≈ 90%, when compared to the nₛ=1 model and the standard ΛCDM. Overall, we find that including the model uncertainty in the considered cases does not significantly impact the Hubble tension.