Abstract
The Goheer–Kleban–Susskind no-go theorem says that the symmetry of de Sitter space is incompatible with finite entropy. The meaning and consequences of the theorem are discussed in light of recent developments in holography and gravitational path integrals. The relation between the GKS theorem, Boltzmann fluctuations, wormholes, and exponentially suppressed non-perturbative phenomena suggests that the classical symmetry between different static patches is broken and that eternal de Sitter space—if it exists at all—is an ensemble average.
Highlights
All phenomena in a region of space can be described by a set of degrees of freedom localized on the boundary of that region, with no more than one degree of freedom per Planck area.The Holographic Principle has been the driving force behind many of the advances in quantum gravity over the last twenty-five years, but to date, the only precise examples have been cosmologies, which, like anti-de-Sitter space, have asymptotically cold1, time-like causal boundaries
Does the Holographic Principle apply to cosmologies such as de Sitter space? If yes, what are the rules? I do not know for sure, and this paper will not conclusively answer the question; I will try to lay out some tentative principles
Occasional Boltzmann fluctuations allow for transitions to higher minima, followed by tunneling back to the lowest minimum. The rates for such fluctuations are of the order exp (−S0), where S0 is the nominal entropy of the de Sitter space at the lowest minimium3
Summary
All phenomena in a region of space can be described by a set of degrees of freedom localized on the boundary of that region, with no more than one degree of freedom per Planck area. The Holographic Principle has been the driving force behind many of the advances in quantum gravity over the last twenty-five years, but to date, the only precise examples have been cosmologies, which, like anti-de-Sitter space, have asymptotically cold, time-like causal boundaries. The reliance on the existence of such boundaries is troubling because the space we livedoes not seem to have them. Instead it has a horizon and a space-like warm boundary. Does the Holographic Principle apply to cosmologies such as de Sitter space? Two things that will not be found here are specific models and applications to phenomenology
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