The Nature of Cosmic Time

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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 time-hypersurface, and each yields the same answer. In this way, one can describe all time choices simultaneously. In an interesting application to cosmology, I compute large-angle microwave background anisotropies and the galaxy-galaxy correlation function associated with the scalar and tensor fluctuations of power-law inflation.