Hartle-Hawking boundary conditions as Nucleation by de Sitter Vacuum

TL;DR

This paper derives the Hartle-Hawking wave function for a de Sitter universe from FLRW equations, explores complex time in cosmology, and proposes a holographic interpretation to address conceptual issues.

Contribution

It introduces a simple derivation of the HH wave function from FLRW models and offers a new holographic interpretation to clarify complex time in cosmology.

Findings

Derivation of HH wave function from FLRW equations

Identification of an oscillator with imaginary time

Proposal of de Sitter Projective Holography as interpretation

Abstract

It is shown that, for a de Sitter Universe, the Hartle-Hawking (HH) wave function can be obtained in a simple way starting from the Friedmann-Lemaitre-Robertson-Walker (FLRW) line element of cosmological equations. An oscillator having imaginary time is indeed derived starting from the Hamiltonian obtaining the HH condition. This proposes again some crucial matter on the meaning of complex time in cosmology. In order to overcome such difficulties, we propose an interpretation of the HH framework based on de Sitter Projective Holography.