Quantum origin of the energy scale of inflation: No-boundary vs tunnelling wavefunctions

Quantum origin of the early inflationary Universe from the no-boundary and tunnelling quantum states is considered in the one-loop approximation of quantum cosmology. A universal effective action algorithm for the distribution function of chaotic inflationary cosmologies is derived for both of these states. The energy scale of inflation is calculated by finding a sharp probability peak in this distribution function for a tunnelling model driven by the inflaton field with large negative constant xi of nonminimal interaction. The sub-Planckian parameters of this peak (the mean value of the corresponding Hubble constant H similar or equal to: 10(-5)m(P), its quantum width Delta H/H similar or equal 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 observational status of inflation theory, provided the coupling constants of the theory are constrained by a condition which is likely to be enforced by the (quasi) supersymmetric nature of the sub-Planckian particle physics model.