Information-theoretic model selection applied to supernovae data

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 cosmological model to the model selection. In this paper we apply information-theoretic model selection approach based on Akaike criterion as an estimator of Kullback-Leibler entropy. In particular, we present the proper way of ranking the competing models based on Akaike weights (in Bayesian language - posterior probabilities of the models). Out of many particular models of dark energy we focus on four: quintessence, quintessence with time varying equation of state, brane-world and generalized Chaplygin gas model and test them on Riess' Gold sample. As a result we obtain that the best model - in terms of 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. One can also notice that models similar in structure i.e. $\Lambda$CDM, quintessence and quintessence with variable equation of state are closer to each other in terms of Kullback-Leibler entropy. Models having different structure i.e. Chaplygin gas or brane-world scenario are more distant (in Kullback-Leibler sense) from the best one.