Quantum Probabilities for Inflation from Holography

TL;DR

This paper explores how the quantum state of the universe, described by the Wheeler-DeWitt equation, relates asymptotically to anti-de Sitter and de Sitter geometries, establishing a holographic connection for quantum probabilities of inflation.

Contribution

It demonstrates a universal semiclassical structure linking quantum cosmology with holography, connecting de Sitter probabilities to anti-de Sitter configurations.

Findings

Quantum probabilities for de Sitter histories derive from anti-de Sitter actions.

Solutions of the Wheeler-DeWitt equation have asymptotically real geometries.

A universal holographic relation between quantum cosmology and AdS/CFT is established.

Abstract

The evolution of the universe is determined by its quantum state. The wave function of the universe obeys the constraints of general relativity and in particular the Wheeler-DeWitt equation (WDWE). For non-zero \Lambda, we show that solutions of the WDWE at large volume have two domains in which geometries and fields are asymptotically real. In one the histories are Euclidean asymptotically anti-de Sitter, in the other they are Lorentzian asymptotically classical de Sitter. Further, the universal complex semiclassical asymptotic structure of solutions of the WDWE implies that the leading order in \hbar quantum probabilities for classical, asymptotically de Sitter histories can be obtained from the action of asymptotically anti-de Sitter configurations. This leads to a promising, universal connection between quantum cosmology and holography.