Abstract
We complete an old argument that causal diamonds in the crunching region of the Lorentzian continuation of a Coleman-Deluccia instanton for transitions out of de Sitter space have finite area, and provide quantum models consistent with the principle of detailed balance, which can mimic the instanton transition probabilities for the cases where this diamond is larger or smaller than the causal patch of de Sitter space. We review arguments that potentials which do not have a positive energy theorem when the lowest de Sitter minimum is shifted to zero, may not correspond to real models of quantum gravity.
Highlights
As an example, the development of the AdS/CFT correspondence has provided us with a convincing collection of models of quantum gravity with AdS boundary conditions
Our conclusion will be that there is a large class of Lagrangians, which admit CDL transitions between dS spaces with different radii and dS spaces and a Big Crunch, that are compatible with being a semi-classical description of a quantum system in a finite dimensional Hilbert space, whose maximal entropy is of order the Gibbons-Hawking entropy of the largest dS point
These are models whose potential is above the Great Divide: when a constant is added to make the c.c. in the lowest dS minimum vanish, there is no instanton transition because the Minkowski solution obeys the positive energy theorem
Summary
The development of the AdS/CFT correspondence has provided us with a convincing collection of models of quantum gravity with AdS boundary conditions. These are models whose potential is above the Great Divide: when a constant is added to make the c.c. in the lowest dS minimum vanish, there is no instanton transition because the Minkowski solution obeys the positive energy theorem.
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