Classical Spacetime from Quantum Gravity

We show how classical spacetime emerges from quantum gravity through the study of a quantum FRW cosmological model coupled to a free massive scalar field using a new asymptotic expansion method of the Wheeler-DeWitt equation. It is shown that the coherent states of the nonadiabatic basis of a particular generalized invariant give rise to the quantum back reaction of matter field proportional to classical energy and the Einstein-Hamilton-Jacobi with matter becomes equivalent to the classical Einstein equation. Classical and Qauntum Gravity 13, in press Electronic address: [email protected] 1 In recent years, apart from the attempt to endow canonical gravity with a quantum gravity theory by overcoming many conceptual and technical problems, quantum cosmology has also been used to derive semiclassical gravity in which one has the quantum field theory in a curved spacetime and the classical Einstein equation with the expectation value of quantum matter field. If canonical quantum gravity in the form of the Wheeler-DeWitt (WD) equation is to have successful and useful applications in cosmology, there should be a consistent limiting procedure from a supposed quantum gravity written formally as Ĝμν = 8πκT̂μν , in which both the gravity and matter field are quantized at the same time and κ is the gravitation constant, first to the semiclassical gravity written also formally as Gμν = 8πκ 〈