BARYON AND TIME ASYMMETRIES OF THE UNIVERSE

This paper is devoted to the investigation of connection between two apparent asymmetries of the nature --- time-asymmetry and Baryon Asymmetry of the Universe (BAU). The brief review of this subjects is given. We consider the particle behavior in curved space-time and the possibility of $T$- and $CPT$-violation by the universe expansion. If these symmetries are violated we can dispens with the nonequilibrium condition which is usualy considered as the one of necessary ingredients for BAU-generation. Such mechanism of GUT-scale baryogenesis can provide the observed value of baryon asymmetry. We show this on the example of minimal $SU(5)$ model which usually fails to explain the observed BAU withought taking into account gravitational effects. Predominance of matter over antimatter and the cosmological arrow of time (the time-direction in which the Universe expands) seem to be connected facts and, possibly, BAU is the one of observable facts of $CPT$-violation in nature.