Should we doubt the cosmological constant?

• Published in: Monthly notices of the Royal Astronomical Society Vol. 410; no. 4; pp. 2488 - 2496
• Main Authors: March, M. C., Starkman, G. D., Trotta, R., Vaudrevange, P. M.
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01-02-2011; Wiley-Blackwell; Oxford University Press
• Subjects: Astronomy; Astrophysics; Bayesian analysis; Cosmological constant; cosmological parameters; Dark energy; Dark matter; Earth, ocean, space; Exact sciences and technology; Mathematical models; methods: statistical; supernovae: type Ia; methods: statistical; dark energy; cosmological parameters; supernovae: type Ia; Probability; Statistical method; Type I supernova; Cosmological constant; Upper bound; Equations of state; Statistical models; Energy equation; Cosmological parameter; Cold dark matter; Cosmology; Dark energy; Bayes methods; Performance; Cosmological models
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1111/j.1365-2966.2010.17614.x

While Bayesian model selection is a useful tool to discriminate between competing cosmological models, it only gives a relative rather than an absolute measure of how good a model is. Bayesian doubt introduces an unknown benchmark model against which the known models are compared, thereby obtaining an absolute measure of model performance in a Bayesian framework. We apply this new methodology to the problem of the dark energy equation of state, comparing an absolute upper bound on the Bayesian evidence for a presently unknown dark energy model against a collection of known models including a flat Lambda cold dark matter (ΛCDM) scenario. We find a strong absolute upper bound to the Bayes factor B between the unknown model and ΛCDM, giving B≲ 5. The posterior probability for doubt is found to be less than 13 per cent (with a 1 per cent prior doubt) while the probability for ΛCDM rises from an initial 25 per cent to almost 70 per cent in light of the data. We conclude that ΛCDM remains a sufficient phenomenological description of currently available observations and that there is little statistical room for model improvement.