The Self-Organized Critical Multiverse

Abstract

Recently a dynamical selection mechanism for vacua based on search optimization was proposed in the context of false-vacuum eternal inflation on the landscape. The search algorithm, defined by local vacuum transitions, is optimal in regions of the landscape where the dynamics are tuned at criticality, with de Sitter vacua having an average lifetime of order their Page time. The purpose of this paper is to shed light on the nature of the dynamical phase transition at the Page lifetime. We focus on a finite region of the landscape, which exchanges volume with the rest of the landscape and as such acts as an open system. Through a change of variables the master equation governing the comoving volume of de Sitter vacua is mapped to a stochastic equation for coupled overdamped stochastic oscillators -- the well-known Ornstein-Uhlenbeck process. The rest of the landscape, which acts as an environment, is assumed to result in a non-vanishing driving term for all sites in the region with uncorrelated, white noise fluctuations (though not necessarily Gaussian). We first show that the static susceptibility of the oscillators diverges as the average lifetime of de Sitter vacua approaches the Page time. Thus, optimal regions of the landscape are most susceptible to volume influx from their environing landscape. We then show that the displacement fluctuations for the oscillators exhibit a $1/f$ power spectrum over a broad range of frequencies, precisely at the critical Page lifetime distribution. A $1/f$ power spectrum is a hallmark of non-equilibrium systems at criticality. In analogy with sand avalanches in the abelian sandpile or neuronal avalanches in the brain, de Sitter vacua at criticality can be thought of as undergoing scale invariant volume fluctuation avalanches.

arXiv comment14 pages. v2: Added appendix describing time evolution of driving term; version published in JCAP

References in corpus (24)

• Measuring Information Transfer
• de Sitter Vacua in String Theory
• Quantization of Four-form Fluxes and Dynamical Neutralization of the Cosmological Constant
• Information in Black Hole Radiation
• Are biological systems poised at criticality?
• Higgs mass implications on the stability of the electroweak vacuum
• Probabilities in the inflationary multiverse
• Recycling universe
• Computational complexity of the landscape I
• Scale Invariant Instantons and the Complete Lifetime of the Standard Model
• A Priori Probability Distribution of the Cosmological Constant
• Are We Typical?
• Probabilities in the Bousso-Polchinski multiverse
• The Volume of the Universe after Inflation and de Sitter Entropy
• Computational Complexity of Vacua and Near-Vacua in Field and String Theory
• Science in a Very Large Universe
• Vacuum Selection from Cosmology on Networks of String Geometries
• Universality of the Volume Bound in Slow-Roll Eternal Inflation
• Asymptotic Symmetries in de Sitter and Inflationary Spacetimes
• Miracles and complementarity in de Sitter space
• On Thermalization in de Sitter Space
• Accessibility Measure for Eternal Inflation: Dynamical Criticality and Higgs Metastability
• Patient Observers and Non-perturbative Infrared Dynamics in Inflation
• Neuroevolution on the Edge of Chaos

Cited by in corpus (12)

• Stochastic Inflation at NNLO
• Self-Organised Localisation
• A New Paradigm for Precision Top Physics: Weighing the Top with Energy Correlators
• Yoga Dark Energy: Natural Relaxation and Other Dark Implications of a Supersymmetric Gravity Sector
• Gauge hierarchy from electroweak vacuum metastability
• Higgs Criticality beyond the Standard Model
• Gravity-improved metastability bounds for the Type-I Seesaw Mechanism
• Early-Time Measure in Eternal Inflation
• Bayesian Reasoning in Eternal Inflation: A Solution to the Measure Problem
• Attenuation of Cosmic Ray Electron Boosted Dark Matter
• Hubble selection of the weak scale from QCD quantum critical point
• Gauge hierarchy and metastability from Higgs-driven crunching