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

Abstract

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 $\hat{I}›$CDM model, considering a varying curvature density parameter $\hat{I}{\text{c◯}}_{\mathrm{k}}$, a spectral index ${\mathrm{n}}_{\mathrm{s}}=1$ and a varying $n_{\mathrm{run}}$, a constant dark energy equation of state (EOS) $w_0$CDM and a time-dependent one $w_0{w}_a$CDM. We also test cosmological data against a varying effective number of neutrino species $N_{\mathrm{eff}}$. 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 $\hat{I}›$CDM model is favoured when combining CMB data with CMB lensing, BAO and Bicep-KECK 2018 data against $K-\hat{I}›$CDM model $N_{\mathrm{eff}}-\hat{I}›$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 $\hat{I}›$CDM model and the constant dark energy EOS model $w_0$CDM, with an approximately split model posterior probability of $\approx 60\%:40\%$ in favour of $\hat{I}›$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 $n_{\mathrm{run}}$, with a probability $\approx 90\%$, when compared to the $n_{\mathrm{s}}=1$ model and the standard $\hat{I}›$CDM. Overall, we find that including the model uncertainty in the considered cases does not significantly impact the Hubble tension.