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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 CDM model, considering a varying curvature density parameter ₊, a spectral index n ₒ=1 with running dn ₒ/dk, a constant dark energy equation of state (EOS) w₀-CDM and a time-dependent one w₀wₐ-CDM. We also test cosmological data against a varying effective number of neutrino species N ₄₅₅. 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 CDM model is favoured when combining CMB data with CMB lensing, BAO and Bicep-KECK 2018 data against k-CDM model N ₄₅₅-CDM 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 CDM model and the constant dark energy EOS model w₀-CDM, with an approximately split model posterior probability of 60\%: 40\% in favour of CDM, 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 dn ₒ/dk, with a probability 90\%, when compared to the n ₒ=1 model and the standard CDM. Overall, we find that including the model uncertainty in the considered cases does not significantly impact the Hubble tension.
Paradiso et al. (Mon,) studied this question.