Holographic Tunneling Wave Function

TL;DR

This paper establishes a holographic correspondence between the tunneling wave function in cosmology and the partition function of deformed CFTs on AdS boundaries, providing new insights into quantum cosmology and holography.

Contribution

It demonstrates the equivalence of the tunneling wave function with the AdS wave function and computes the partition function of deformed O(N) models, linking holography with cosmological wave functions.

Findings

The holographic tunneling wave function is related to CFT partition functions.

Partition functions of deformed O(N) models qualitatively match cosmological wave functions.

Inhomogeneity amplitudes are not damped in the holographic tunneling state.

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.