The usual theory of inflation breaks down in eternal inflation. They derive a dual description of eternal inflation in terms of a deformed CFT located at the threshold of eternal inflation. The partition function gives the amplitude of different geometries of the threshold surface in the HartleHawking 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.
The evidence of the multiverse should be measurable in cosmic microwave background radiation. A deep-space probe with the right sensors on-board could measure it with enough precision.
Eternal inflation is a near de Sitter regime deep into the phase of inflation in which the quantum fluctuations in the energy density of the inflaton are large. In the usual account of eternal inflation the quantum diffusion dynamics of the fluctuations is modeled as stochastic effects around a classical slow roll background. Since the stochastic effects dominate the classical slow roll it is argued eternal inflation produces universes that are globally highly irregular, with exceedingly large or infinite constant density surfaces.
However this account is questionable, because the dynamics of eternal inflation wipes out the separation into classical backgrounds and quantum fluctuations that is assumed. We therefore put forward a different model of eternal inflation based on gauge-gravity duality. A reliable theory of eternal inflation is important to sharpen the predictions of slow roll inflation. This is because the dynamics of eternal inflation specifies the prior over the zero modes, or slow roll backgrounds, in the theory which in turn determines its predictions for the precise spectral properties of CMB fluctuations on observable scales.
They have used gauge-gravity duality to describe the quantum dynamics of eternal inflation in the no-boundary state in terms of a dual field theory defined on a global constant density surface in the large volume limit. Working with the semiclassical form of dS/CFT the field theories are Euclidean AdS/CFT duals deformed by a low dimension scalar operator that is sourced by the bulk scalar driving eternal inflation.
The inverse of the partition function specifies the amplitude of different shapes of the conformal boundary surface. This yields a holographic measure on the global structure of eternally inflating universes. We have computed this explicitly in a toy model consisting of a mass deformed interacting O(N) vector theory defined on squashed spheres. In this model we find that the amplitude is low for geometries far from the round conformal structure. These include surfaces with negative scalar curvature which, we have argued, are strongly suppressed in a holographic measure in general. Based on this we conjecture that eternal inflation produces universes that are relatively regular on the largest scales. This is radically different from the usual picture of eternal inflation arising from a semiclassical gravity treatment.
Their conjecture strengthens the intuition that holographic cosmology implies a significant reduction of the multiverse to a much more limited set of possible universes. This has important implications for anthropic reasoning. In a significantly constrained multiverse discrete parameters are determined by the theory. Anthropic arguments apply only to a subset of continuously varying parameters, such as the amount of slow roll inflation. However, the setup we have considered does not allow us to describe the transition from the quantum realm of eternal inflation to a universe in the semiclassical gravity domain. This is because our duals are defined in the UV and live at future infinity. It therefore remains an open question whether the conjectured smoothness of global constant density surfaces impacts the eternity of eternal inflation. To answer this will require a significant extension of holographic cosmology to more realistic cosmologies. It has been suggested that in such models, inflation corresponds to an IR fixed point of the theory. The detailed exit from inflation will then be encoded in the coupling between the field theory degrees of freedom and the bulk dynamics in a manner somewhat analogous to the holographic description of vacuum decay in AdS.