Search Optimization, Funnel Topography, and Dynamical Criticality on the String Landscape

Abstract

A striking feature of our universe is its near criticality. The cosmological constant and weak hierarchy problems, as well as the metastability of the electroweak vacuum, can all be understood as problems of criticality. This suggests a statistical physics approach, based on the string landscape. We present a dynamical selection mechanism for hospitable vacua based on search optimization. Instead of focusing on stationary probability distributions, we are interested in the approach to equilibrium. This is particularly relevant if cosmological evolution has occurred for a time shorter than the exponentially-long mixing time for the landscape. This imposes a strong selection pressure among hospitable vacua, favoring those in regions where the search algorithm is efficient. Specifically, the mean first passage time is minimized for hospitable vacua lying at the bottom of funnel-like regions, akin to the smooth folding funnels of proteins and the loss functions of well-trained deep neural networks. The optimality criterion is time-reparametrization invariant and defined by two competing requirements: search efficiency, which requires minimizing the mean first passage time, and sweeping exploration, which requires that random walks are recurrent. Optimal landscape regions reach a compromise by lying at the critical boundary between recurrence and transience, thereby achieving dynamical criticality. Remarkably, this implies that the optimal lifetime of vacua coincides with the de Sitter Page time. Our mechanism makes concrete phenomenological predictions: 1. The expected lifetime of our universe is $10^{130}$ years, which is ~$2\sigma$ from the Standard Model metastability estimate; 2. The SUSY breaking scale should be high, $>10^{10}$ GeV. The present framework suggests a correspondence between the near-criticality of our universe and non-equilibrium critical phenomena on the landscape.

35 pages, 2 figures. v2: References added

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• 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
• Statistical Predictions in String Theory and Deep Generative Models
• Accessibility Measure for Eternal Inflation: Dynamical Criticality and Higgs Metastability
• Primordial Black Holes as Dark Matter through Higgs Criticality
• Early-Time Measure in Eternal Inflation
• Gravity-improved metastability bounds for the Type-I Seesaw Mechanism
• Bayesian Reasoning in Eternal Inflation: A Solution to the Measure Problem
• Hubble selection of the weak scale from QCD quantum critical point
• Gauge hierarchy and metastability from Higgs-driven crunching