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De Sitter Space Without Dynamical Quantum Fluctuations

May 1, 2014

34 pages

Published in:

Found.Phys. 46 (2016) 6, 702-735

Published: Mar 10, 2016

e-Print:

1405.0298 [hep-th]

DOI:

10.1007/s10701-016-9996-8

Report number:

CALT-68-2878

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Abstract: (Springer)

We argue that, under certain plausible assumptions, de Sitter space settles into a quiescent vacuum in which there are no dynamical quantum fluctuations. Such fluctuations require either an evolving microstate, or time-dependent histories of out-of-equilibrium recording devices, which we argue are absent in stationary states. For a massive scalar field in a fixed de Sitter background, the cosmic no-hair theorem implies that the state of the patch approaches the vacuum, where there are no fluctuations. We argue that an analogous conclusion holds whenever a patch of de Sitter is embedded in a larger theory with an infinite-dimensional Hilbert space, including semiclassical quantum gravity with false vacua or complementarity in theories with at least one Minkowski vacuum. This reasoning provides an escape from the Boltzmann brain problem in such theories. It also implies that vacuum states do not uptunnel to higher-energy vacua and that perturbations do not decohere while slow-roll inflation occurs, suggesting that eternal inflation is much less common than often supposed. On the other hand, if a de Sitter patch is a closed system with a finite-dimensional Hilbert space, there will be Poincaré recurrences and dynamical Boltzmann fluctuations into lower-entropy states. Our analysis does not alter the conventional understanding of the origin of density fluctuations from primordial inflation, since reheating naturally generates a high-entropy environment and leads to decoherence, nor does it affect the existence of non-dynamical vacuum fluctuations such as those that give rise to the Casimir effect.

Note:

version accepted for publication in Foundations of Physics

Cosmology
Foundations of quantum mechanics
Everett (Many-Worlds) interpretation
Quantum fluctuations
space: de Sitter
fluctuation: quantum
vacuum state
field theory: scalar: massive
background: de Sitter
hair

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