http://arxiv.org/abs/1706.07784
We investigate Euclidean complexified wormholes in de Sitter space. It is known that for a suitable choice of parameters, the probability for the occurrence of the wormhole configuration can be higher than that for the compact instanton, and hence the Hartle-Hawking wave function will be dominated by Euclidean wormholes. Such wormhole configuration can be interpreted as the creation of two classical universes from nothing. In order to classicalize both universes and to connect at least one with inflation, it is necessary that the inflaton potential be specified. We numerically investigate the situation and find that only one end of the wormhole can be classicalized for a convex inflaton potential such as the chaotic inflation model with $\phi^{2}$ potential, while both ends can be classicalized for a concave potential such as the Starobinsky-type $R^{2}$ inflation model. Therefore, if (1) the boundary condition of our universe is determined by the Hartle-Hawking wave function, (2) Euclidean wormholes dominate the contribution to the path integral, and (3) the classicality condition must be satisfied at both ends, then we conclude that it is more probable that our universe began with a concave rather than a convex inflation, which may explain the Planck Mission data.
P. Chen and D. Yeom
Mon, 26 Jun 17
8/40
Comments: 5 pages, 2 figures
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