A description of the open universe model by the Bessel functions

For the open models of Universe there are solutions both for a noncoherent dust and for an equilibrium radiation which are written in a parametric form in a comoving synchronous reference frame. In the first place the parametric description makes many difficulties for an investigation. Secondly, the each from mentioned cosmological solutions of the gravitational equations is correctly only for the concrete interval of the time parameter change. And one from two solutions can not be converted to another solution because these solutions belong to different equations of state. In other words the each solution describes the concrete substance. Therefore it is desirable to find solution which must exclude both above said remarks. By such an example can be the exact solution of the Einstein equations for the open cosmological model with radiation. This solution describes an asymptotical behaviour for the large times of the coherent dust (with a zero pressure) and the equilibrium radiation with an equation of state for ultrarelativistic gas. Such solution belongs to the Bessel functions class. In the paper the open cosmological model with a negative scalar curvature is considered. A metric is taken in Fock’s form as the conformal metric to the Minkowski metric (the conformally Galilean metric). Such choice of metric let us to write the gravitational equations in more simple form. The exact solution of the gravitational cosmological equations can be found in the Bessel functions’ class. The investigation of the open cosmological model with dust and radiation leads to a statement that the "purely electromagnetic "model of Universe (without a substance) is an unstable model. This cosmological model is reduced into stable cosmological model by small portions of the substance. So this physically means that the open Universe can not exist without the substance.