Inflation, evidence and falsifiability

In this paper we consider the issue of paradigm evaluation by applying Bayes' theorem along the following nested chain of progressively more complex structures: i) parameter estimation (within a model), ii) model selection and comparison (within a paradigm), iii) paradigm evaluation. In such a chain the Bayesian evidence works both as the posterior's normalization at a given level and as the likelihood function at the next level up. Whilst raising no objections to the standard application of the procedure at the two lowest levels, we argue that it should receive an essential modification when evaluating paradigms, in view of the issue of falsifiability. By considering toy models we illustrate how unfalsifiable models and paradigms are always favoured by the Bayes factor. We argue that the evidence for a paradigm should not only be high for a given dataset, but exceptional with respect to what it would have been, had the data been different. We propose a measure of falsifiability (which we term predictivity), and a prior to be incorporated into the Bayesian framework, suitably penalising unfalsifiability. We apply this measure to inflation seen as a whole, and to a scenario where a specific inflationary model is hypothetically deemed as the only one viable as a result of information alien to cosmology (e.g. Solar System gravity experiments, or particle physics input). We conclude that cosmic inflation is currently difficult to falsify and thus to be construed as a scientific theory, but that this could change were external/additional information to cosmology to select one of its many models. We also compare this state of affairs to bimetric varying speed of light cosmology.