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Journal Article

Wave function of simple universes analytically continued from negative to positive potentials


Lehners,  Jean-Luc
Theoretical Cosmology, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Lehners, J.-L. (2021). Wave function of simple universes analytically continued from negative to positive potentials. Physical Review D, 104(6): 063527. doi:10.1103/PhysRevD.104.063527.

Cite as: http://hdl.handle.net/21.11116/0000-0008-B5FA-2
We elaborate on the correspondence between the canonical partition function in asymptotically AdS universes and the no-boundary proposal for positive vacuum energy. For the case of a pure cosmological constant, the analytic continuation of the AdS partition function is seen to define the no-boundary wave function (in dS) uniquely in the simplest minisuperspace model. A consideration of the AdS gravitational path integral implies that on the dS side, saddle points with Hawking-Moss/Coleman-De Luccia-type tunnelling geometries are irrelevant. This implies that simple topology changing geometries do not contribute to the nucleation of the universe. The analytic AdS/dS equivalence holds up once tensor fluctuations are added. It also works, at the level of the saddle point approximation, when a scalar field with a mass term is included, though in the latter case, it is the mass that must be analytically continued. Our results illustrate the emergence of time from space by means of a Stokes phenomenon, in the case of positive vacuum energy. Furthermore, we arrive at a new characterisation of the no-boundary condition, namely that there should be no momentum flux at the nucleation of the universe.