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One proposal for dS/CFT is that the Hartle-Hawking (HH) wave function in thelarge volume limit is equal to the partition function of a Euclidean CFTdeformed by various operators. All saddle points defining the semiclassical HHwave function in cosmology have a representation in which their interiorgeometry is part of a Euclidean AdS domain wall with complex matter fields. Wecompute the wave functions of scalar and tensor perturbations aroundhomogeneous isotropic complex saddle points, turning on single scalar fieldmatter only. We compare their predictions for the spectra of CMB perturbationswith those of a different dS/CFT proposal based on the analytic continuation ofinflationary universes to real asymptotically AdS domain walls. We find thepredictions of both bulk calculations agree to first order in the slow rollparameters, but there is a difference at higher order which, we argue, is asignature of the HH state of the fluctuations.

Primordial fluctuations from complex AdS saddle points