A nonsingular oneloop wave function of the universe from a new eigenvalue asymptotics in quantum gravity
Abstract
Recent work on euclidean quantum gravity on the fourball has proved regularity at the origin of the generalized ζfunction built from eigenvalues for metric and ghost modes, when diffeomorphisminvariant boundary conditions are imposed in the de Donder gauge. The hardest part of the analysis involves one of the four sectors for scalartype perturbations, the eigenvalues of which are obtained by squaring up roots of a linear combination of Bessel functions of integer adjacent orders, with a coefficient of linear combination depending on the unknown roots. This paper obtains, first, approximate analytic formulae for such roots for all values of the order of Bessel functions. For this purpose, both the descending series for Bessel functions and their uniform asymptotic expansion at large order are used. The resulting generalized ζfunction is also built, and another check of regularity at the origin is obtained. For the first time in the literature on quantum gravity on manifolds with boundary, a vanishing oneloop wave function of the Universe is found in the limit of small threegeometry, which suggests a quantum avoidance of the cosmological singularity driven by full diffeomorphism invariance of the boundaryvalue problem for oneloop quantum theory.
 Publication:

Journal of High Energy Physics
 Pub Date:
 September 2005
 DOI:
 10.1088/11266708/2005/09/063
 arXiv:
 arXiv:hepth/0507264
 Bibcode:
 2005JHEP...09..063E
 Keywords:

 High Energy Physics  Theory
 EPrint:
 21 Pages, Latex and .eps files with JHEP3 style. The discussion in Section 5 has been improved, and Ref. 26 has been added