Nonlinear solutions of long-wavelength gravitational radiation

In a significant improvement over homogeneous minisuperspace models, it is shown that the classical nonlinear evolution of inhomogeneous scalar fields and the metric is tractable when the wavelength of the fluctuations is larger than the Hubble radius. Neglecting second-order spatial gradients, one can solve the energy constraint as well as the evolution equations by invoking a transformation to new canonical variables. The Hamilton-Jacobi equation is separable and complete solutions are given for gravitational radiation and multiple scalar fields interacting through an exponential potential. Although the time parameter is arbitrary, the natural choice is the determinant of the three-metric. The momentum constraint may be simply expressed in terms of the new canonical variables which define the spatial coordinates. The long-wavelength analysis is essential for a proper formulation of stochastic inflation which enables one to model non-Gaussian primordial fluctuations for structure formation.