A Measure of De Sitter Entropy and Eternal Inflation
A Measure of de Sitter Entropy and Eternal Inflation Nima Arkani-Hameda, Sergei Dubovskya,b, Alberto Nicolisa, Enrico Trincherinia, and Giovanni Villadoroa a Jefferson Physical Laboratory, Harvard University, Cambridge, MA 02138, USA b Institute for Nuclear Research of the Russian Academy of Sciences, 60th October Anniversary Prospect, 7a, 117312 Moscow, Russia Abstract We show that in any model of non-eternal inflation satisfying the null energy condition, the area of the de Sitter horizon increases by at least one Planck unit in each inflationary e-folding. This observation gives an operational meaning to the finiteness of the entropy SdS of an inflationary de Sitter space eventually exiting into an asymptotically flat region: the asymptotic observer is never able to measure more than eSdS independent inflationary modes. This suggests a limitation on the amount of de Sitter space outside the horizon that can be consistently described at the semiclassical level, fitting well with other examples of the breakdown of locality in quantum gravity, such as in black hole evaporation. The bound does not hold in models of inflation that violate the null energy condition, such as ghost inflation. This strengthens the case for the thermodynamical interpretation of the bound as conventional black hole thermodynamics also fails in these models, strongly suggesting that arXiv:0704.1814v1 [hep-th] 13 Apr 2007 these theories are incompatible with basic gravitational principles. 1 Introduction String theory appears to have a landscape of vacua [1, 2], and eternal inflation [3, 4] is a plausible mechanism for populating them. In this picture there is an infinite volume of spacetime undergoing eternal inflation, nucleating bubbles of other vacua that either themselves eternally inflate, or end in asymptotically flat or AdS crunch space-times.
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