Abstract
In the long-wavelength approximation, a general set of semiclassical wave functionals is given for gravity and matter interacting in 3+1 dimensions. In the long-wavelength theory, one neglects second-order spatial gradients in the energy constraint. These solutions satisfy the Hamilton-Jacobi equation, the momentum constraint, and the equation of continuity. It is essential to introduce inhomogeneities to discuss the role of time. The time hypersurface is chosen to be a homogeneous field in the wave functional. It is shown how to introduce tracer particles through a dust field into the dynamical system. The formalism can be used to describe stochastic inflation.
- Received 16 February 1993
DOI:https://doi.org/10.1103/PhysRevD.48.719
©1993 American Physical Society