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Bayesian evidence and predictivity of the inflationary paradigm

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Title: Bayesian evidence and predictivity of the inflationary paradigm
Authors: Gubitosi, G
Lagos, M
Magueijo, J
Allison, R
Item Type: Journal Article
Abstract: 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 posteriors 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.
Issue Date: 1-Jun-2016
Date of Acceptance: 24-May-2016
URI: http://hdl.handle.net/10044/1/34358
DOI: https://dx.doi.org/10.1088/1475-7516/2016/06/002
ISSN: 1475-7516
Publisher: IOP Publishing
Journal / Book Title: Journal of Cosmology and Astroparticle Physics
Volume: 2016
Issue: June 2016
Copyright Statement: ©2016 IOP Publishing Ltd. Giulia Gubitosi et al JCAP06(2016)002
Keywords: astro-ph.CO
gr-qc
hep-ph
Nuclear & Particles Physics
0201 Astronomical And Space Sciences
0202 Atomic, Molecular, Nuclear, Particle And Plasma Physics
Notes: Final version with corrections added
Publication Status: Published
Appears in Collections:Physics
Theoretical Physics
Faculty of Natural Sciences



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