STAROBINSKY MODEL WITH A VISCOUS FLUID

Abstract

The article considers some cosmological solutions of the Starobinsky model for a flat inhomogeneous viscous Universe. The first section contains a brief of the F(R)  theory of gravity. One of the most common examples of F(R) gravity with a high degree of curvature is the Starobinsky model. For the Starobinsky  F(R)=aR+bR² model, the cosmological model of a flat and homogeneous Universe is considered. For the Friedmann-Robertson-Walker metric, the Lagrange function is defined, and the corresponding equations are determined by the Euler-Lagrange equations and the Hamilton energy condition. Using the equation of state for inhomogeneous viscous fluid, we considered two cases of the viscosity parameter when the state parameter is constant. Next, using the results obtained, we determined the dynamics of the Hubble parameter H. At constant viscosity,  has a negative value of the Hubble parameter and decreases with time along a hyperbola, while the viscosity parameter with proportional dependence on H has a positive value that decreases along a hyperbola.

If we compare it with the well-known de Sitter solution describing the accelerated expansion of the Universe and take into account that time in physics should only be positive, then the change in the Hubble parameter for the viscosity with proportional dependence on H occurs later. An analysis of this solution shows that at a certain point in time the acceleration of the Universe turns into a process of instantaneous compression. However, in the end, the result is similar to the de Sitter solution tends to zero, i.e. the Universe stops accelerating. Based on the results obtained, a graph was constructed with respect to the de Sitter solution. The analysis was carried out according to the graph. These results are useful for describing the accelerated expansion of the modern Universe and do not contradict modern astronomical observations.