Abstract <p>The gauge gravitation theory in the Riemann–Cartan space-time is investigated in order to solve the fundamental problems of the general relativity theory. The constraints on indefinite parameters of the theory, under which the solutions of isotropic cosmology describe a nonsingular accelerating Universe, are given. Numerical solutions of cosmological equations are obtained near the limiting energy density at a transition from gravitational compression to expansion, in dependence on the energy density, in the case of flat, closed and open models. Some physical and astrophysical consequences of the gauge gravitational theory in Riemann–Cartan space-time are discussed.</p>