Information theoretic model selection applied to supernovae data

Current advances in observational cosmology suggest that our Universe is flat and dominated by dark energy. There are several different theoretical ideas invoked to explain the 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 from estimating specific parameters of the cosmological model to the model selection.

In this paper we apply an information theoretic model selection approach based on the Akaike criterion as an estimator of Kullback Leibler entropy. Although this approach has already been used by some authors in a similar context, this paper provides a more systematic introduction to the Akaike criterion. In particular, we present the proper way of ranking the competing models on the basis of Akaike weights (in Bayesian language: posterior probabilities of the models). This important ingredient is lacking from alternative studies dealing with cosmological applications of the Akaike criterion.

Of the many particular models of dark energy we focus on four: quintessence, quintessence with a time varying equation of state, the braneworld scenario and the generalized Chaplygin 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 the quintessence model. The odds suggest that although there exist differences in the support given to specific scenarios by supernova data, most of the models considered receive similar support. The only exception is the Chaplygin gas which is considerably 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 in terms of Kullback Leibler entropy. Models having different structure, e.g. Chaplygin gas and the braneworld scenario, are more distant (in the Kullback Leibler sense) from the best one.