* Astronomy

Title: No evidence for extensions to the standard cosmological model
Author: Alan Heavens, Yabebal Fantaye, Elena Sellentin, Hans Eggers, Zafiirah Hosenie, Steve Kroon, Arrykrishna Mootoovaloo

We compute the Bayesian Evidence for the theoretical models considered in the main analysis of Planck cosmic microwave background data. By utilising carefully-defined nearest-neighbour distances in parameter space, we reuse the Monte Carlo Markov Chains already produced for parameter inference to compute Bayes factors B for many different models and with many different datasets from Planck with and without ancillary data. When CMB lensing is included, we find that the standard 6-parameter flat Lambda CDM model is favoured over all other models considered, with curvature being mildly favoured when CMB lensing is not included. We also conclude that many alternative models are strongly disfavoured by the data. These include strong evidence against primordial correlated isocurvature models (lnB=-8.0), non-zero scalar-to-tensor ratio (lnB=-4.3), running of the spectral index (lnB=-4.7), curvature (lnB=-3.6), non-standard numbers of neutrinos (lnB=-3.1), non-standard neutrino masses (lnB=-3.2), non-standard lensing potential (lnB=-3.9), evolving dark energy (lnB=-3.2), sterile neutrinos (lnB=-7.0), and extra sterile neutrinos with a non-zero scalar-to-tensor ratio (lnB=-10.8). Other models are less strongly disfavoured with respect to flat Lambda CDM. As with all analyses based on Bayesian Evidence, the final numbers depend on the widths of the parameter priors. We adopt for our calculations the priors used in the Planck parameter inference analyses themselves while performing a sensitivity analysis for two of the best competitor extensions. The resulting message is nevertheless clear: current data favour the standard flat Lambda CDM model. Our quantitative conclusion is that extensions beyond the standard cosmological model are strongly disfavoured, even where they are introduced to explain tensions or anomalies.

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