Accelerated Expansion of the Universe in Terms of Differential Spaces

Abstract

The concept of closures of manifolds in the category of Sikorski’s differential spaces is applied to a description of the flat FRWmodels. The smoothness condition coming from this approach constitutes a strong restriction on the time dependence of the scale factor and on the energy density of the matter content of the resulting model. We demonstrate that our model agrees with the H(z) dependence obtained with the help observational data concerning the type Ia supernovae, BAO and the CMB peaks tests. The model contains a string gas, two types of domain walls, four types of cosmological vacuums and a cosmological constant whose value — determined by the model — agrees with the results of the Planck Mission.