From DeWitt initial condition to cosmological quantum entanglement

At the classical level, a linear dilaton action offers an eternal inflation evolution governed by the unified (cosmological constant plus radiation) equation of state ρ- 3P = 4. At the quantum mechanical mini-superspace level, a two-particle variant of the no-boundary proposal, notably one-particle energy dependent, is encountered. While a (gravityanti-gravity) GaG-odd wave function can only host a weak Big Bang (BB) boundary condition, albeit for any k, a strong BB boundary condition requires a GaG-even entangled wave function, and singles out k = 0 flat space. The locally maximal values for the cosmological scale factor a and the inverse Newton constant φ form a grid {a2, a } ∼√4n 1 +1 √4n2+1.