Cosmological zoo—accelerating models with dark energy

Abstract

Recent observations of type Ia supernovae indicate that the Universe is in an acceleratingphase of expansion. The fundamental quest in theoretical cosmology is to identify theorigin of this phenomenon. In principle there are two possibilities: (1) the presence of matterwhich violates the strong energy condition (a substantial form of dark energy) or(2) modified Friedmann equations (Cardassian models—a non-substantial form ofdark matter). We classify all these models in terms of two-dimensional dynamicalsystems of the Newtonian type. We search for generic properties of the models. It isachieved with the help of Peixoto’s theorem for dynamical systems on the Poincarésphere. We find that the notion of structural stability can be useful to distinguishthe generic cases of evolutional paths with acceleration. We find that, while theΛCDM models and phantom models are typical accelerating models, the cosmological models withbouncing phase are non-generic in the space of all planar dynamical systems. We derive theuniversal shape of the potential function which gives rise to presently accelerating models.Our results show explicitly the advantages of using the potential function (instead of theequation of state) to probe the origin of the present acceleration. We argue that simplicityand genericity are the best guide in understanding our Universe and its acceleration.