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Abstract
The usual theory of inflation breaks down in eternal inflation. We derive a dual description of eternal inflation in terms of a deformed Euclidean CFT located at the threshold of eternal inflation. The partition function gives the amplitude of different geometries of the threshold surface in the no-boundary state. Its local and global behavior in dual toy models shows that the amplitude is low for surfaces which are not nearly conformal to the round three-sphere and essentially zero for surfaces with negative curvature. Based on this we conjecture that the exit from eternal inflation does not produce an infinite fractal-like multiverse, but is finite and reasonably smooth.
Highlights
This transforms the probability distribution for the amount of inflation and leads to the prediction that our universe emerged from a regime of eternal inflation [12, 13]
Working with the semiclassical form (1.1) of dS/CFT the dual field theories involved are Euclidean AdS/CFT duals deformed by a complex low dimension scalar operator sourced by the bulk scalar driving eternal inflation
The inverse of the partition function specifies the amplitude of different shapes of the conformal boundary at the exit from scalar field eternal inflation
Summary
For definiteness we start with the well known consistent truncation of M-theory on AdS4 × S7 down to Einstein gravity coupled to a single scalar φ with potential. Fefferman-Graham expansion implies that in terms of the variable r the asymptotically (Lorentzian) dS domain of the theory is to be found along the vertical line τ = r + iπ/2 in the complex τ -plane [18] This is illustrated in figure 1 where r changes from real to imaginary values along the horizontal branch of the AdS contour from xA to xT P. It is usually argued that the typical individual histories described by this wave function develop highly irregular constant density surfaces with a configuration of bubble-like regions with locally negative curvature We revisit this from a holographic viewpoint. Whilst we formally define our dual on the exit surface Σf from scalar field eternal inflation, at υ in figure 1, we might as well take υ → ∞ because the classical, asymptotic Λ-phase amounts to an overall volume rescaling of the boundary surface which preserves the relative probabilities of different conformal bopundary geometries [18]
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