Towards a quantum theory of long-wavelength gravity

Details Towards a quantum theory of long-wavelength gravity Towards a quantum theory of long-wavelength gravity

Nov 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992phrvd..46.4373s&link_type=abstract

Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 46, Issue 10, 15 November 1992, pp.4373-4386

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Scientific paper

A quantum theory of long-wavelength gravity interacting with a dust field χ is proposed in 3+1 dimensions. These models are superior to homogeneous minisuperspace models of quantum cosmology because they describe the nonlinear quantum evolution of inhomogeneities. In addition, they may be used to describe the late stages of gravitational collapse. For a special choice of operator ordering, a wave functional Ψ is given which satisfies both the energy constraint as well as the momentum constraint. The positive probability ||Ψ||2 is conserved on time hypersurfaces where the dust field is uniform. Explicit Green's function solutions are given. If one considers an ad hoc potential V(χ) which is a function of the dust field, one can discuss the quantum mechanics of dust-driven inflation. The initial conditions for the long-wavelength wave functional arise from short-wavelength quantum processes. The statistics of the wave functional may possibly be tested in cosmic microwave background anisotropy experiments.

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