CLASSICAL SPACETIME FROM QUANTUM-GRAVITY

We show how classical spacetime emerges from quantum gravity through t he study of a quantum FRW cosmological model coupled to a free massive scalar field using a new asymptotic expansion method of the Wheeler-D eWitt equation. It is shown that the coherent states of the nonadiabat ic basis of a particular generalized invariant give rise to the quantu m back reaction of the matter field, which is proportional to the clas sical energy, and the Einstein-Hamilton-Jacobi equation with a matter field becomes equivalent to the classical Einstein equation.