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### THE OPEN UNIVERSE MODEL WITH THE COSMOLOGICAL CONSTANT AS APARTICLE MOVEMENT TASK IN A FORCE FIELD

#### Baranov A. M., Saveljev E.V.

The possibility of deriving of exact cosmological solutions of the Einstein equations with the cosmological constant for the open universe model by reducing the problem to an equivalent task of the movement of a mass particle in the force field is considered. Taken cosmological model is filled by substance in an approximation of the perfect fluid with nonzero pressure and cosmological constant, generally speaking. A four-dimensional space-time metric is taken in Fock’s form as the metric, conformal to the Minkowski metric. This metric depends on one variable. A square of the variable is a product of advanced and retarded times. The using of mechanical interpretation of the gravitation equations leads to a possibility of consideration of various force fields, in particular the potential fields, with the subsequent physical interpretation of found exact cosmological solutions. First of all the movement of free particle with an unit mass (a mechanical force is absent) is considered, that is to say the particle moves on inertia. The fourth degree of finded law of movement is a conformal factor of cosmological conformally-flat metric. This case corresponds to the exact cosmological solution without cosmological constant and pressure, coinciding with known the Friedman solution for the open universe. After that the force potential is taken in the form of linear function. Found exact cosmological solution asymptotically describes both an incoherent dust, and the ultra-relativistic matter which could be interpreted as an equilibrium radiation. Further a square-law function without a linear term and a stationary value is taken as a potential. Such potential can be interpreted as potential of the free oscillator corresponding to linear shift force (Hooke’s force). The solution of corresponding equation of motion is written in the form of a cosine function with some initial phase related to the correlation of parameters which define dust-like and ultra-relativistic matter. The cosmological model is the generalization of Friedman’s model with the equilibrium radiation and substance which fill the universe. Examples of models in the presence of the cosmological constant are considered.

** Keywords:** The open universe models, a "mechanical" approach to the construction of cosmological models, the cosmological constant

** UDC:** 530.12; 530.51

** PACS:** 04.20.-q; 98.80.Jk

** DOI:** 10.17238/issn2226-8812.2023.3-4.21-29

*Please cite this article in English as:*

Baranov A.M., Saveljev E.V. The open universe model with the cosmological constant as a particle movement task in a force field. Space, Time and Fundamental Interactions, 2023, no. 3-4, pp. 21-29.