Primordial fluctuations from complex AdS saddle points
  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.
