Bayesian evidence and predictivity of the inflationary paradigm
  In this paper we consider the issue of paradigm evaluation by applying Bayes'
theorem along the following nested hierarchy 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 hierarchy
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 a considerable modification when
evaluating paradigms, when testability and fitting data are equally important.
By considering toy models we illustrate how models and paradigms that are
difficult to falsify 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. With this motivation we propose a measure which we term
predictivity, as well as a prior to be incorporated into the Bayesian
framework, penalising unpredictivity as much as not fitting data. 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 hard to
falsify, 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.
