Here, 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. Furthermore, we postulate 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.
Boddy, Kimberly K., et al. "De Sitter Space Without Dynamical Quantum Fluctuations." Foundations of Physics, vol. 46, no. 6, Mar. 2016. https://doi.org/10.1007/s10701-016-9996-8
Boddy, Kimberly K., Carroll, Sean M., & Pollack, Jason (2016). De Sitter Space Without Dynamical Quantum Fluctuations. Foundations of Physics, 46(6). https://doi.org/10.1007/s10701-016-9996-8
Boddy, Kimberly K., Carroll, Sean M., and Pollack, Jason, "De Sitter Space Without Dynamical Quantum Fluctuations," Foundations of Physics 46, no. 6 (2016), https://doi.org/10.1007/s10701-016-9996-8
@article{osti_1596697,
author = {Boddy, Kimberly K. and Carroll, Sean M. and Pollack, Jason},
title = {De Sitter Space Without Dynamical Quantum Fluctuations},
annote = {Here, 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. Furthermore, we postulate 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.},
doi = {10.1007/s10701-016-9996-8},
url = {https://www.osti.gov/biblio/1596697},
journal = {Foundations of Physics},
issn = {ISSN 0015-9018},
number = {6},
volume = {46},
place = {United States},
publisher = {Springer},
year = {2016},
month = {03}}
Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 356, Issue 1743https://doi.org/10.1098/rsta.1998.0250