Classical Spacetime from Quantum Gravity

We elaborate the recently introduced asymptotically exact semiclassical quantum gravity derived from the Wheeler-DeWitt equation by finding a particular coherent state representation of a quantum scalar field in which the back-reaction of the scalar field Hamiltonian exactly gives rise to the classical one. In this coherent state representation classical spacetime emerges naturally from semiclassical quantum gravity.

Using the coherent-state representation we show that the classical Einstein equation for the FRW cosmological model with a general minimal scalar field can be derived from the semiclassical quantum Einstein equation.

A new asymptotic expansion method is developed to separate the Wheeler-DeWitt equation into the time-dependent Schr\"{o}dinger equation for a matter field and the Einstein-Hamilton-Jacobi equation for the gravitational field including the quantum back-reaction of the matter field. In particular, the nonadiabatic basis of the generalized invariant for the matter field Hamiltonian separates the Wheeler-DeWitt equation completely in the asymptotic limit of $m_p^2$ approaching in...

How the time evolution which is typical for classical cosmology emerges from quantum cosmology? The answer is not trivial because the Wheeler-DeWitt equation is time independent. A framework associating the quantum Hamilton-Jacobi to the minisuperspace cosmological models has been introduced in [1]. In this paper, we show that time dependence and quantum-classical correspondence both arise naturally in the quantum Hamilton-Jacobi formalism of quantum mechanics applied to quan...

We study the classical and quantum models of a scalar field Friedmann-Robertson-Walker (FRW) cosmology with an eye to the issue of time problem in quantum cosmology. We introduce a canonical transformation on the scalar field sector of the action such that the momentum conjugate to the new canonical variable appears linearly in the transformed Hamiltonian. Using this canonical transformation, we show that, it may lead to the identification of a time parameter for the correspo...

We consider a Schr\"odinger quantum dynamics for the gravitational field associated to a FRW spacetime and then we solve the corresponding eigenvalue problem. We show that, from a phenomenological point of view, an Evolutionary Quantum Cosmology overlaps the Wheeler-DeWitt approach. We also show how a so peculiar solution can be inferred to describe the more interesting case of a generic cosmological model.

The quantum description of time evolution in non-linear gravitational systems such as cosmological space-times is not well understood. We show, in the simplified setting of mini-superspace, that time evolution of this system can be obtained using a gauge fixed path integral, as long as one does not integrate over proper time. Using this gauge fixed action we can construct a Hamiltonian in the coherent - or classical - state basis. We show that by construction the coherent sta...

The Hamiltonian approach to General Relativity is developed similarly to the Wheeler-DeWitt Hamiltonian cosmology, where the cosmological scale factor is treated as a time-like dynamic variable and its canonical momentum is considered as an evolution generator in the field space of events with the postulate about a physical vacuum as a state with the minimal eigenvalue of this generator. The cosmological scale factor is extracted from the Hamiltonian General Relativity with...

We propose a method to recover the time variable and the classical evolution of the Universe from the minisuperspace wave function of the Wheeler-DeWitt equation. Defining a Hamilton-Jacobi characteristic function $W$ as the imaginary part of the $\ln \Psi$ we can recover the classical solution, and quantum corrections. The key idea is to let the energy of the Wheeler-DeWitt equation vanish only after the semiclassical limit is taken.

Using the ontological interpretation of quantum mechanics in a particular sense, we obtain the classical behaviour of the scale factor and two scalar fields, derived from a string effective action for the FRW time dependent model. Besides, the Wheeler-DeWitt equation is solved exactly. We speculate that the same procedure could also be applied to S-branes.