Information theoretic model selection applied to supernovae data

Abstract

Current advances in observational cosmology suggest that our Universe is flat anddominated by dark energy. There are several different theoretical ideas invoked to explainthe dark energy with relatively little guidance of which one of them might be right.Therefore the emphasis of ongoing and forthcoming research in this field shifts fromestimating specific parameters of the cosmological model to the model selection.In this paper we apply an information theoretic model selection approach based on theAkaike criterion as an estimator of Kullback–Leibler entropy. Although this approach hasalready been used by some authors in a similar context, this paper provides a moresystematic introduction to the Akaike criterion. In particular, we present the proper way ofranking the competing models on the basis of Akaike weights (in Bayesian language:posterior probabilities of the models). This important ingredient is lacking fromalternative studies dealing with cosmological applications of the Akaike criterion.Of the many particular models of dark energy we focus on four: quintessence, quintessencewith a time varying equation of state, the braneworld scenario and the generalizedChaplygin gas model, and test them on Riess’s gold sample.As a result we obtain that the best model—in terms of the Akaike criterion—is thequintessence model. The odds suggest that although there exist differences inthe support given to specific scenarios by supernova data, most of the modelsconsidered receive similar support. The only exception is the Chaplygin gas which isconsiderably less supported. One can also note that models similar in structure,e.g. ΛCDM, quintessence and quintessence with a variable equation of state, are closer to each other interms of Kullback–Leibler entropy. Models having different structure, e.g. Chaplygin gasand the braneworld scenario, are more distant (in the Kullback–Leibler sense) from thebest one.