It is shown that the gravitational theory in 4-dimensional Riemann-Cartan space-time offers opportunities to solve some principal problems of general relativity theory and modern cosmology. In the framework of this theory the gravitational interaction can exhibit both repulsive and the usual attractive character which is found in gravitating matter with positive values of energy density and pressure satisfying the energy dominance condition. The Regular Big Bang inflationary scenario with an accelerating stage of cosmological expansion at asymptotics and the principal role of space-time torsion in this scenario are discussed.

Einsteinian general relativity theory (GR) is the base on the modern theory of gravitational interaction and relativistic cosmology. GR allows to describe different gravitating systems and cosmological models at widely changing scales of physical parameters. At the same time GR possesses certain principal difficulties, which, in particular, appear in cosmology. One of the most principal cosmological problems remains the problem of cosmological singularity (PCS): various cosmological models describing the evolution of the Universe have the beginning in time in the past and in accordance with GR the singular state with divergent energy density and singular metrics appears at the beginning of cosmological expansion. It is because the gravitational interaction for gravitating matter with positive values of energy density and pressure satisfying the energy dominance condition in the frame of GR as well as Newton's theory of gravity has the character of attraction, but never repulsion. The PCS is a particular case of general problem of gravitational singularities of GR. Moreover, to explain observational cosmological data in the framework of GR it is necessary to assume that approximately 95% energy in the Universe is related to some hypothetical kinds of gravitating matter - dark energy and non-baryonic dark matter, and only 5% of it is related to the usual gravitating matter, from which galaxies are formed. As a result, the situation in cosmology and generally in gravitational theory is actually similar to that of physics in the beginning of XX century, when the notion of "ether" was introduced in order to explain various electrodynamic phenomena. The creation of special relativity theory by A. Einstein allowed to solve existed problems without the "ether" notion, and the introduction of the notion of 4-dimensional physical space-time continuum (pseudo-euclidian Minkovski space-time) was of principal physical meaning. The structure of physical space-time is more complicated in the gravitational theory. According to GR it is a 4-dimensional pseudo-Riemannian continuum. The application of gauge approach to gravitation leads to the conclusion that the structure of the physical space-time can be more complicated in comparison with GR: if one supposes that the gauge group corresponding to gravitation includes the Lorentz group and the Lorentz gauge field exists in nature, we obtain necessarily the gravitation theory in the Riemann-Cartan space-time U4 as natural generalization of GR. The corresponding theory is known as the Poincaré gauge theory of gravity (PGTG), in the frame of which the gravitation field is described by means of interacting metric and torsion fields and the role of sources of gravitational field play the energy-momentum and spin tensors of gravitating matter (by using minimum connection between gravitation field and gravitating matter). This talk is devoted to discussion of applying of PGTG in order to solve some indicated problems of GR.