How many parameters in the cosmological models with dark energy?

In cosmology many dramatically different scenarios in the past (big bang versus bounce) and in the future (de Sitter versus big rip) are compatible with the present day observations. This difficulties are called the degeneracy problem. We use the Akaike (AIC) and Bayesian (BIC) information criteria of model selection to avoid this degeneracy and to determine the model with such a set of parameters which gives the most preferred fit to the data. We consider seven representative scenarios, namely: the ACDM, CDM model with topological defect, phantom CDM model, bouncing ACDM model, bouncing phantom CDM model, brane ACDM model and model with the dynamical equation of state parameter linearized around the present epoch. Applying the information criteria to the currently available SNIa data we show that AIC indicates the flat phantom model while BIC indicates both flat phantom CDM and flat ACDM models. Finally we conclude that number of essential parameters chosen by dark energy models which are compared with SNIa data is two. (c) 2005 Elsevier B.V. All rights reserved.