Perturbative quantum cosmology around the scrMscrS(Td) minisuperspace

Details Perturbative quantum cosmology around the scrMscrS(Td) minisuperspace Perturbative quantum cosmology around the scrMscrS(Td) minisuperspace

Feb 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993phrvd..47.1391p&link_type=abstract

Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 47, Issue 4, 15 February 1993, pp.1391-1395

Physics

Scientific paper

We study the Wheeler-DeWitt equation for the cases of first- and second-order perturbations around the scrMscrS(Td) minisuperspace, which is the Wheeler superspace of all flat and orthogonal tori in d dimensions. To first order, the Wheeler-DeWitt equation is an infinite-dimensional globally hyperbolic massless Klein-Gordon equation. A definition of a Hilbert space in that region of superspace is straightforward, but the dynamics is trivial. To second order, the Wheeler-DeWitt equation is an infinite-dimensional globally hyperbolic Klein-Gordon equation, but with a mass-squared term which is time dependent. This time dependence ruins the possibility of a simple definition of a Hilbert space.

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