Friedmanlike model with pressure on the Friedman solution basis for the open universe

In the article a new method of finding of exact solutions on the basis of the Friedman solution for the open Universe in the Fock form is proposed.The known method developed in the previous articles is applied to deriving of an exact solution. This method reduces 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 equation of the Newton second law for function which is a root of the fourth degree from a conformal factor. 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 proportional to the square of the "displacement". 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.This solution is chosen for a basis function, and an integration constant, generally speaking, does not coincide with the Friedman constant. Such function is accepted for a new dimensionless variable. In the end, a class of the solutions depending on a parameter, running row of natural numbers, is obtained. The detailed analysis shows that at one only value of this parameter for discovered solution has physical sense. Near by of the origin of cosmological model expansion the equation of state close to equation of state of the ultrarelativistic gas.In this case cosmological model can be viewed as Friedman-like model with the pressure, disappearing on a Galilean asymptotics, leading to the Friedman open model for the incoherent dust.