Thermodynamics of viscous Matter and Radiation in the Early Universe
  Assuming that the background geometry is filled with free gas consisting of matter and radiation and no phase transitions being occurred in the early Universe, we discuss the thermodynamics of this {\it closed} system using classical approaches. We find that essential cosmological quantities, such as Hubble parameter $H$, scale factor $a$ and curvature parameter $k$, can be derived from this simple model, which on one hand fulfills and entirely obeys the laws of thermodynamics. On the other hand, the results are compatible with the Friedmann-Lemaitre-Robertson-Walker model and the Einstein field equations. The inclusion of finite bulk viscosity coefficient derives to important changes in all these cosmological quantities. Accordingly, our picture about the evolution of the Universe and its astrophysical consequences seems to be a subject of a radical revision. We find that $k$ strongly depends on the thermodynamics of background matter. The time scale, at which negative curvature might take place, depends on the relation between the matter content and the total energy. Using quantum and statistical approaches, we assume that the size of the Universe is given by the volume occupied one particle and one photon. Different types of their interactions are taken into account. Expressions for $H$ and $a$ are introduced. Therefore, the expansion of the Universe turns to be accessible. 
A. Tawfik (Egyptian Ctr. Theor. Phys., Cairo & Freie U., Berlin) and   H. Magdy (Egyptian Ctr. Theor. Phys., Cairo)
gr-qc