On the Problem of Cosmological Singularity within Gauge Theories of Gravitation

In this note I discuss the problem of cosmological singularities within gauge theories of gravitation. Solutions of cosmological equations with the scalar field are considered. The problem of cosmological singularity is one of the most fundamental issues in modern theoretical cosmology. Investigation of this problem within gauge theories of gravitation (GTG) is of undoubted interest, since numerous attempts of resolution of this problem did not reach success within general relativity (GR). Generalized cosmological Freidmann equations (GCFE) were derived in 1980 in [1] within the framework of GTG. It possesses important regularizing properties and allows obtaining nonsingular solutions having friedmannian asymptotics of GR. The study of cosmological models with the scalar field within GTG is motivated by successes of existing inflationary models within GR. The first regular solution with nonlinear scalar field was obtained in [2]. Since analytical solution of GCFE does not exist, the qualitative analysis (by analogy with GR [3]) seems to be promising. It turns out that unlike GR the phase space of the dynamical system, corresponding to GCFE in the case of scalar field, is bounded within GTG [5]. The boundary of the phase space contains special solutions of cosmological equations [4]. The presence of this boundary allows avoiding divergencies of the scalar field derivative with respect to time on contraction stage that take place for most solutions within GR in the finite region for the scalar field. Within GR in simplest cases the stage of cosmological expansion is described by the phase portrait with the stable focus singular point at the origin [3]. On the phase portrait describing contraction stage the corresponding singular point is unstable focus. Moreover, the two phase portraits are independent. In order to locate the solution one has to determine to sign of the Hubble parameter. Within GTG the phase space has much more complicated structure. Close to the origin the phase portraits practically coincide with the corresponding portraits within GR since in this case the GCFE is equivalent to the Friedmann equation. However, according to [4] the Hubble parameter vanishes in the finite region of the phase space within GTG. As a consequence, there are inevitably regular transitions from contraction to expansion and back in the finite region of the phase space even in the case of flat and open type models in addition to close type models within GR. Moreover, the phase space has nontrivial topology: the phase portraits with stable