2018, no. 1

### Once again on the Friedman-like model of open Universe with pressure

#### Baranov A.M.

In this article there is a development of a new method of finding of exact solutions on the basis of the Friedman solution for the open Universe in the Fock form. This method was proposed in the previous article. Besides this the approach is closely connected with another method which allows to reduce the modelling problem of the open Universe with the conformally flat metric in the Fock form to a problem of mechanical moving of a particle in the given force field. In this case the Einstein equations with an energy-momentum tensor in an approximation of a Pascal perfect fluid are transformed to the equation similar to the second law of Newton for function which is a root of the fourth degree of conformal factor. In this case analog of "force"is proportional to the pressure. This "force"is chosen in the form of the linear law with a variable "stiffness"coefficient which is inversely to the square of the "displacement". This "displacement"is a new variable here which is connected with the Fiedman solution for the open Universe. When the "force"equals zero, the equation solution is equal to the solution for the Friedman open cosmological model in the Fock form for an incoherent dust. The solution is chosen as a basis function, and an integration constant, generally speaking, coincides with the Friedman constant only for a concrete value of parameter of a model. As the result a family of solutions of cosmological equations is found for discrete values of function of state into the Universe origin (in the sense of new variable) for physically interpreted cases. All found solutions have the Friedman asymptotic. In such cases were constructed two tables with functions of state and conformal factors. In the article the graphs of functions of state and conformal factors were also made in these cases. There is the most low state with equation of state of relativistic strings.

Keywords: ñonstruction of cosmological models, exact open cosmological solutions, function of state, the open Universe evolution.

UDC: 530.12; 530.51

PACS: 04.20.-q; 04.20.Cv

DOI: 10.17238/issn2226-8812.2018.1.4-12