On one integrable cosmological model of the flat universe in k-essence
Myrzakulov K.R. Kenzhalin D.Zh. Myrzakul T.R.
22 December 2021al-Farabi Kazakh State National University
International Journal of Mathematics and Physics
2021#12Issue 287 - 92 pp.
The study of the origin and evolution of our Universe is one of the interesting and actual directions in modern physics and astrophysics. This paper considers the cosmological model of the Universe in the Einsteins theory of gravity and k-essence, where the gravitational field interacts in a non-minimal way with the scalar field φ. That is, in action, in the role of the matter field, we consider the special case of the Lagrange function for the essence. The corresponding field equations of the considered model are obtained. Also, particular solutions for the scale factor a(t) were obtained in the form of de Sitters solution. Two solutions were found, for the potential energy V(t) and the scalar field φ(t), and their graphical solutions were also built. The analytical solutions obtained in this work are solutions of the considered integrable systems. These solutions are in good agreement with the available observational data and are able to describe the modern dynamics of the expansion of the Universe.
action , cosmological model of the Universe , Euler-Lagrange equations , expanding Universe , flat Universe , gravitational field , gravitational theory , integrable cosmological models , k-essence , metric , scalar field
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L.N. Gumilyov Eurasian National University, Nur-Sultan, Kazakhstan
LLP Ratbay Myrzakulov Eurasian International Center for Theoretical Physics, Nur-Sultan, Kazakhstan
L.N. Gumilyov Eurasian National University
LLP Ratbay Myrzakulov Eurasian International Center for Theoretical Physics
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