FROM INSTANTON TO INFLATIONARY UNIVERSE

The present paper is based on a theory which includes gravity and a complex scalar field [ I.M. Khalatnikov and A. Mezhlumian, Phys. Lett. A 169 ( 1992) 308 ]. It is shown that in such a theory we can proceed the evolution from instantons in the classically forbidden (euclidean) region in minisuperspace to the inflationary universe in the classically allowed (Minkowski) region. The characteristics for the Hamilton-Jacobi equation, which define the action in the quasiclassical approximation, are described by four differential equations of first order. This four-dimensional dynamical system was integrated numerically. In the euclidean compact region we found two types of instantons. It is shown that the instantons correspond to extremal trajectories. The existence of two types of instantons gives different possibilities for tunneling from euclidean to Minkowski regions and for creation of inflationary universes.