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Semiclassical Wheeler-DeWitt equation: Solutions for long-wavelength fields

1993; American Physical Society; Volume: 48; Issue: 2 Linguagem: Inglês

10.1103/physrevd.48.719

1538-4500

D. S. Salopek, John M. Stewart, J. Parry,

Advanced Thermodynamics and Statistical Mechanics

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 $\ensuremath{\chi}$ into the dynamical system. The formalism can be used to describe stochastic inflation.