Abstract

I discuss some of the fundamentals of the Hartle-Hawking no-boundary wave function and what it predicts for our cosmological observations. First, I show that the fluctuation convergence criterion recently revived by Kontsevich, Segal and Witten, when applied to complex no-boundary saddles, acts as an inflaton selection mechanism that effectively bounds the tensor-to-scalar ratio of CMB fluctuations to be less than 0.08, in line with current observations. Second, I show that the conditioning and coarse-graining needed to extract predictions for local observations in the no-boundary state induce a Page-like transition that tilts the probability distribution towards a large number of inflationary efolds. Finally, I present a holographic formulation of the wave function that, I conjecture, may be a stepping stone to define the theory beyond the semiclassical approximation. Evidence in favor of this comes from a calculation of the quantum corrections to the entropy of de Sitter space computed using the AdS/CFT correspondence.