QUANTUM ORIGIN OF THE ENERGY SCALE OF INFLATION - NO-BOUNDARY VS TUNNELING WAVE-FUNCTIONS

Quantum origin of the early inflationary Universe from the no-boundary and tunnelling quantum states is considered in the one-loop approxima tion of quantum cosmology. A universal effective action algorithm for the distribution function of chaotic inflationary cosmologies is deriv ed for both of these states. The energy scale of inflation is calculat ed by finding a sharp probability peak in this distribution function f or a tunnelling model driven by the inflaton field with large negative constant xi of nonminimal interaction. The sub-Planckian parameters o f this peak (the mean value of the corresponding Hubble constant H sim ilar or equal to: 10(-5)m(P), its quantum width Delta H/H similar or e qual to 10(-5) and the number of inflationary e-foldings N similar or equal to 60) are found to be in good correspondence with the observati onal status of inflation theory, provided the coupling constants of th e theory are constrained by a condition which is likely to be enforced by the (quasi) supersymmetric nature of the sub-Planckian particle ph ysics model.