Holographic No-Boundary Measure

TL;DR

This paper presents a holographic approach to the no-boundary wave function in cosmology, connecting Euclidean AdS domain walls with Lorentzian de Sitter universes, and proposes a dual CFT description.

Contribution

It introduces a dual formulation of the no-boundary measure using AdS/CFT correspondence, linking Euclidean AdS geometries to inflationary de Sitter universes.

Findings

Regular Euclidean AdS domain walls transition smoothly to Lorentzian de Sitter universes.

The no-boundary measure can be expressed via partition functions of deformed CFTs.

The duality conjecture extends beyond leading order approximations.

Abstract

We show that the complex saddle points of the no-boundary wave function with a positive cosmological constant and a positive scalar potential have a representation in which the geometry consists of a regular Euclidean AdS domain wall that makes a smooth transition to a Lorentzian, inflationary universe that is asymptotically deSitter. The transition region between AdS and dS regulates the volume divergences of the AdS action and accounts for the phases that explain the classical behavior of the final configuration. This leads to a dual formulation in which the semiclassical no-boundary measure is given in terms of the partition function of field theories on the final boundary that are certain relevant deformations of the CFTs that occur in AdS/CFT. We conjecture that the resulting dS/CFT duality holds also beyond the leading order approximation.