Primordial fluctuations from complex AdS saddle points

TL;DR

This paper explores the connection between the Hartle-Hawking wave function in cosmology and Euclidean AdS domain walls, analyzing scalar and tensor perturbations to compare different dS/CFT proposals and identify higher-order differences.

Contribution

It introduces a method to compute cosmological perturbations around complex AdS saddle points and compares predictions of two dS/CFT models, highlighting higher-order discrepancies.

Findings

First-order agreement in spectra predictions

Higher-order differences suggest HH state signatures

Validation of complex saddle point approach

Abstract

One proposal for dS/CFT is that the Hartle-Hawking (HH) wave function in the large volume limit is equal to the partition function of a Euclidean CFT deformed by various operators. All saddle points defining the semiclassical HH wave function in cosmology have a representation in which their interior geometry is part of a Euclidean AdS domain wall with complex matter fields. We compute the wave functions of scalar and tensor perturbations around homogeneous isotropic complex saddle points, turning on single scalar field matter only. We compare their predictions for the spectra of CMB perturbations with those of a different dS/CFT proposal based on the analytic continuation of inflationary universes to real asymptotically AdS domain walls. We find the predictions of both bulk calculations agree to first order in the slow roll parameters, but there is a difference at higher order which, we argue, is a signature of the HH state of the fluctuations.