Resolving the Question of Time for Semiclassical Gravity

Hamilton-Jacobi theory provides a natural starting point for a covariant description of the gravitational field. Using a spatial gradient expansion, one may solve for the phase of the wavefunction by using a line-integral in superspace. Each contour of integration corresponds to a particular choice of the time-hypersurface, and each yields the same answer. In this way, one can describe all time choices simultaneously. As a demonstration of the formalism, I will compute large-angle microwave background anisotropies and the galaxy-galaxy correlation function associated with scalar and tensor fluctuations of power-law inflation.