Abstract
The Hartle-Hawking wave function in cosmology can be viewed as a decaying wave function with anti-de Sitter (AdS) boundary conditions. We show that the growing wave function in AdS familiar from Euclidean AdS/CFT is equivalent, semiclassically and up to surface terms, to the tunneling wave function in cosmology. The cosmological measure in the tunneling state is given by the partition function of certain relevant deformations of CFTs on a locally AdS boundary. We compute the partition function of finite constant mass deformations of the O(N) vector model on the round three sphere and show this qualitatively reproduces the behaviour of the tunneling wave function in Einstein gravity coupled to a positive cosmological constant and a massive scalar. We find the amplitudes of inhomogeneities are not damped in the holographic tunneling state.
Highlights
DS merely compensates for the volume terms in the anti-de Sitter (AdS) action and accounts for the phases that explain the classical behavior of the final configuration [8]
We show that the growing wave function in AdS familiar from Euclidean AdS/CFT is equivalent, semiclassically and up to surface terms, to the tunneling wave function in cosmology
We find the partition functions in both cases qualitatively agree with the behaviour of the minisuperspace tunneling wave function in Einstein gravity coupled to a positive cosmological constant and a massive scalar field, and we interpret this as evidence in favour of our proposal
Summary
We consider Einstein gravity coupled to a positive cosmological constant Λ and a scalar field moving in a positive potential V. This is in sharp contrast with the Hartle-Hawking boundary conditions which select the growing solution under the barrier This yields a real linear combination of ingoing and outgoing waves in the large volume region, describing a time-symmetric ensemble of contracting and expanding universes. Relative probabilities in the Hartle-Hawking state are specified by the amplitude of the growing solution when it emerges from the classically forbidden region As a result both wave functions differ in their predictions: the tunneling wave function (2.4) favours universes in which the scalar field starts high up its potential, leading to a long period of inflation, whereas the Hartle-Hawking wave function favours histories with a low amount of inflation [24].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
