Abstract
A brief review of the Hamiltonian theory of self-gravitating perfect fluid, which has been established by Kijowski et al. (Phys Rev D 41:1875, 1990), has been discussed in this work. The formulation of the spherically symmetric cosmological problem has been derived. The most general three-dimensional metric in the case of spherically symmetric space-time has been considered. In addition, the parameters that govern the dynamics have been fixed. The problem of homogeneous universe has been considered for the ultrarelativistic ideal gas. The dynamical equations have been derived. Three analytical solutions have been obtained.