Thermodynamics in the Viscous Early Universe

Assuming that the matter filling the background geometry in the Early Universe was a free gas and no phase transitions took place, we discuss the thermodynamics of this closed system using classical approaches. We found that essential cosmological quantities, such as the Hubble parameter $H$, the scaling factor $a$ and the curvature parameter $k$, can be derived from this simple model. The results are compatible with the Friedmann-Robertson-Walker model and Einstein field equations. Including finite bulk viscosity coefficient leads to important changes in the cosmological quantities. Accordingly, our picture about evolution of the Universe and its astrophysical consequences seems to be a subject of radical revision. We found that $k$ strongly depends on thermodynamics of the cosmic 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 introduced expressions for $H$ and the bulk viscosity coefficient.