SEMICLASSICAL WHEELER-DEWITT EQUATION - SOLUTIONS FOR LONG-WAVELENGTH FIELDS

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 chi into the dynamical system. The formalism can be used to describe stochastic inflation.