2006/10/09 by Marek Szydlowski, Marek Szydłowski
Physics and Astronomy · #Cosmology #Cosmology and Gravitation Theories #Dark energy #Dark matter #Dynamical systems theory #Inflation (cosmology) #Parameter space #Phase space #Pulsars and Gravitational Waves Research #Relativity and Gravitational Theory #Simplicity #Universe #astro-ph
paper · pdf · doi:10.1088/1475-7516/2007/09/007
published as JCAP 0709:007,2007 · RevTeX4, 23 pages, 10 figures
arxiv created 2006/10/09 · openalex publication_date 2007/09/07 · arxiv updated 2014/10/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Recent observations of type Ia supernovae indicate that the Universe is in an accelerating phase of expansion. The fundamental quest in theoretical cosmology is to identify the origin of this phenomenon. In principle there are two possibilities: (1) the presence of matter which violates the strong energy condition (a substantial form of dark energy) or (2) modified Friedmann equations (Cardassian models—a non-substantial form of dark matter). We classify all these models in terms of two-dimensional dynamical systems of the Newtonian type. We search for generic properties of the models. It is achieved with the help of Peixoto's theorem for dynamical systems on the Poincaré sphere. We find that the notion of structural stability can be useful to distinguish the generic cases of evolutional paths with acceleration. We find that, while the ΛCDM models and phantom models are typical accelerating models, the cosmological models with bouncing phase are non-generic in the space of all planar dynamical systems. We derive the universal 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 the equation of state) to probe the origin of the present acceleration. We argue that simplicity and genericity are the best guide in understanding our Universe and its acceleration.