Qualitative Analysis and Numerical Simulation of Equations of the Standard Cosmological Model

Abstract

On the basis of qualitative theory of differential equations it is shown that dynamic system based on the system of Einstein - Klein - Gordon equations with regard to Friedman Universe has a stable center corresponding to zero values of scalar potential and its derivative at infinity. Thus, the cosmological model based on single massive classical scalar field in infinite future would give a flat Universe. The carried out numerical simulation of the dynamic system corresponding to the system of Einstein - Klein - Gordon equations showed that at great times of the evolution the invariant cosmological acceleration has a microscopic oscillating character ($T\sim 2\pi mt$), while macroscopic value of the cosmological acceleration varies from $+1$ at inflation stage after which if decreases fast to $-1/2$ (non-relativistic stage), and then slowly tends to $-1$ (ultrarelativistic stage).

arXiv comment27 pages, 28 figures, 8 references

References in corpus (1)

• Instability Model of the Universe with De Sitter Beginning

Cited by in corpus (3)

• A macroscopic view to the standard cosmological model
• The Peculiarities of the Cosmological Models Based on Nonlinear Classical and Phantom Fields with Minimal Interaction. II. The Cosmological Model Based on the Asymmetrical Scalar Doublet
• The Peculiarities of the Cosmological Models Based on Non-Linear Classical and Phantom Fields with Minimal Interaction. I. The Cosmological Model Based on Scalar Singlet