Quantum Trans-Planckian Origin of the Universe and Multiverses

We describe the Universe quantum asymptotic gravitational Vaccua: the initial (in) Vaccum {\it "Nothing"}, the late Vacuum State, ({\it "Everything"}) today, and connect them through a unitary $S$\,- Matrix as a Classical-Quantum Dual Transform across the Planck scale. The {\bf minimal} or initial time and {\bf entropy} are in the range \,$0 < t_{in} \leq 10^{-61}\; t_P$,\, and \, $0 < \;S_{in} \leq \;10^{-122}$ \,($t_P$, \, and $s_P$ \, being their Planck values). The late time and entropy being : $ t_{today} = 10^{-61}\;\, t_P \leq t_{late} \leq t_{max}$, \,$S_{\,today} = 10^{122}\,\leq \,S_{late} \le S_{\,max}$. The gravitationnal phase transitions in this context are discussed, early and last stages of expansion and contraction (bangs and crunchs). The Initial Vacuum is a quantum gravitational foam of borning and dying (crushing) universes, quantum and decaying black holes, particles and or strings and radiation. The truly quantum gravity (trans-Planckian) gravitational entropy $S_Q = 10^{-122}$ {\it dominates} the tunneling probability from "Nothing", which is almost equal to $1$,\, strongly supporting the Universe "birth" as a quantum tunneling from the Vacuum. (In the non-complete picture the gravitational euclidean action is classical/semiclassical with huge value $S_{\Lambda} = 10^{+122} $ and extremely small tunneling, while in the {\it complete quantum picture} the effect is the {\it opposite}). The global quantum de Sitter space-time is found : A new and quantum Penrose-de Sitter diagram and the physical spectrum covering all gravity domains. There are {\bf no singularities} of any kind here. The imaginary time {\it quantum} de Sitter instanton is complete. The quantum gravity partition function, temperature and entropy all reflect this feature. These results are all non-perturbative, and strongly support the feature that a complete quantum theory of gravity is a {\it finite theory}, which is much more than a renormalizable theory, and {\it a theory of pure numbers}.