STAROBINSKY MODEL WITH A VISCOUS FLUID
Open Access
- 1 June 2022
- journal article
- research article
- Published by al-Farabi Kazakh National University in International Journal of Mathematics and Physics
- Vol. 13 (1), 99-104
- https://doi.org/10.26577/ijmph.2022.v13.i1.011
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.Keywords
This publication has 13 references indexed in Scilit:
- Cosmology of f-essence with inhomogeneous viscous fluidJournal of Physics: Conference Series, 2019
- Reconstruction of k-essence inflation in Horndeski gravityThe European Physical Journal Plus, 2017
- k $k$ -essence in Horndeski modelsAstrophysics and Space Science, 2016
- Inhomogeneous fluids for warm inflationAstrophysics and Space Science, 2015
- Coupled fluids model in FRW space-timeAstrophysics and Space Science, 2014
- Interacting Quintessence Models of Dark EnergyInternational Journal of Theoretical Physics, 2014
- Inhomogeneous viscous fluids in FRW universe and finite-future time singularitiesAstrophysics and Space Science, 2014
- FRW and Bianchi type I cosmology of f-essenceAstrophysics and Space Science, 2011
- G-essence cosmologies with scalar-fermion interactionsThe European Physical Journal Plus, 2011
- The development of perturbations in the universe described by the nonstationary equation of stateRussian Physics Journal, 2009