Quantum Origin of the Early Universe and the Energy Scale of Inflation

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 {\mbox{\boldmathH}}\simeq 10^{-5}m_P, its quantum width \Delta{\mbox{\boldmathH}}/{\mbox{\boldmathH$}}\simeq 10^{-5}$andthenumberofinflationarye-foldings${\mbox{\boldmath $N$}}\simeq 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.