The (No) Boundary Proposal and excited states in de Sitter holography

TL;DR

This paper explores the extension of the no boundary proposal in de Sitter holography to include excited states by adding boundaries and boundary conditions, affecting late-time cosmological observables and advancing the holographic dictionary.

Contribution

It introduces a method to define excited states in de Sitter holography through boundary conditions, expanding the no boundary proposal beyond the ground state.

Findings

Consistent computation of n-point functions with excited states.

Late-time observables are modified in these excited states.

Potential implications for the holographic dictionary in de Sitter space.

Abstract

In the AdS/CFT framework, vacuum and excited states are systematically described by imposing arbitrary Dirichlet boundary conditions at the AdS boundary. Furthermore, there are explicit relations connecting the quantum states to their corresponding dual Euclidean AdS geometries, in line with the Hartle-Hawking (HH) construction. The ground state therefore corresponds to the dominant saddle point under trivial conditions on the asymptotic boundary, which is the exact Euclidean AdS geometry. In contrast, the situation in de Sitter spacetime differs significantly, as there is no natural region analogous to the AdS boundary. Thus, the Hartle Hawking approach precisely defines the ground state as a path integral over smooth (Euclidean) geometries ending on a spatial Cauchy surface, with \textit{no} additional boundary or past singularity, known as the no boundary proposal. In this work, we revisit the no boundary proposal to describe excited states within the framework of de Sitter Holography. Specifically, we investigate the possibility of defining a family of excited states by introducing an additional boundary in the Euclidean region and imposing arbitrary Dirichlet boundary conditions on it. As a result, we demonstrate that the computation of $n$ point correlation functions is consistent with the presence of excited states, and furthermore, show that cosmological late-time observables in these states undergo non-trivial modifications. This study may have significant implications for the development of the holographic dictionary for de Sitter spacetimes.