Early-Time Measure in Eternal Inflation

Abstract

In a situation like eternal inflation, where our data is replicated at infinitely-many other space-time events, it is necessary to make a prior assumption about our location to extract predictions. The principle of mediocrity entails that we live at asymptotic late times, when the occupational probabilities of vacua has settled to a near-equilibrium distribution. In this paper we further develop the idea that we instead exist during the approach to equilibrium, much earlier than the exponentially-long mixing time. In this case we are most likely to reside in vacua that are easily accessed dynamically. Using first-passage statistics, we prove that vacua that maximize their space-time volume at early times have: 1. maximal ever-hitting probability; 2. minimal mean first-passage time; and 3. minimal decay rate. These requirements are succinctly captured by an early-time measure. The idea that we live at early times is a predictive guiding principle, with many phenomenological implications. First, our vacuum should lie deep in a funneled region, akin to folding energy landscapes of proteins. Second, optimal landscape regions are characterized by relatively short-lived vacua, with lifetime of order the de Sitter Page time. For our vacuum, this lifetime is $\sim 10^{130}$~years, which is consistent with the Standard Model estimate due to Higgs metastability. Third, the measure favors vacua with small, positive vacuum energy. This can address the cosmological constant problem, provided there are sufficiently many vacua in the entire ensemble of funnels. As a concrete example, we study the Bousso-Polchinski lattice of flux vacua, and find that the early-time measure favors lattices with the fewest number of flux dimensions. This favors compactifications with a large hierarchy between the lightest modulus and all other Kähler and complex structure moduli.

arXiv comment34 pages, 3 figures

References in corpus (80)

• Hierarchies from Fluxes in String Compactifications
• Axions In String Theory
• Quantization of Four-form Fluxes and Dynamical Neutralization of the Cosmological Constant
• Higgs mass and vacuum stability in the Standard Model at NNLO
• The dS/CFT Correspondence
• Information in Black Hole Radiation
• Investigating the near-criticality of the Higgs boson
• Universality classes in nonequilibrium lattice systems
• On the Cosmological Implications of the String Swampland
• From the Big Bang Theory to the Theory of a Stationary Universe
• On weakly turbulent instability of anti-de Sitter space
• De Sitter Space and the Swampland
• On the metastability of the Standard Model vacuum
• Predictions from Quantum Cosmology
• Eternal inflation and its implications
• Disturbing Implications of a Cosmological Constant
• Improved Higgs Mass Stability Bound in the Standard Model and Implications for Supersymmetry
• On the Possibility of Large Axion Decay Constants
• Stability of the Electroweak Vacuum: Gauge Independence and Advanced Precision
• Cosmological implications of the Higgs mass measurement
• The Probable Fate of the Standard Model
• Correlation Functions in Stochastic Inflation
• The network topology of a potential energy landscape: A static scale-free network
• Can the universe afford inflation?
• Probabilities in the inflationary multiverse
• IMPROVED METASTABILITY BOUNDS ON THE STANDARD MODEL HIGGS MASS
• Holographic probabilities in eternal inflation
• Generation of fluctuations during inflation: comparison of stochastic and field-theoretic approaches
• A Measure of de Sitter Entropy and Eternal Inflation
• Fluctuations of the Gravitational Constant in the Inflationary Brans-Dicke Cosmology
• The lifetime of the electroweak vacuum and sensitivity to Planck scale physics
• Boltzmann brains and the scale-factor cutoff measure of the multiverse
• Recycling universe
• Computational complexity of the landscape I
• Stationary Universe
• Stochastic growth of quantum fluctuations during slow-roll inflation
• Scale Invariant Instantons and the Complete Lifetime of the Standard Model
• Living Dangerously with Low-Energy Supersymmetry
• Consistent Use of the Standard Model Effective Potential
• Properties of the scale factor measure
• On the distribution of stable de Sitter vacua
• Making predictions in the multiverse
• Is Our Universe Likely to Decay within 20 Billion Years?
• A Priori Probability Distribution of the Cosmological Constant
• Are We Typical?
• Probabilities in the Bousso-Polchinski multiverse
• The Phase Transition to Eternal Inflation
• Multiple Fields in Stochastic Inflation
• Prediction and explanation in the multiverse
• Critical Number of Fields in Stochastic Inflation
• Self-Organised Localisation
• The Volume of the Universe after Inflation and de Sitter Entropy
• Higher-order scalar interactions and SM vacuum stability
• Computational Complexity of Vacua and Near-Vacua in Field and String Theory
• Approximating tunneling rates in multi-dimensional field spaces
• Vacuum Selection from Cosmology on Networks of String Geometries
• Science in a Very Large Universe
• Universality of the Volume Bound in Slow-Roll Eternal Inflation
• Asymptotic Symmetries in de Sitter and Inflationary Spacetimes
• Tunneling in Stochastic Inflation
• Miracles and complementarity in de Sitter space
• Stationary configurations of the Standard Model Higgs potential: electroweak stability and rising inflection point
• Gauge hierarchy from electroweak vacuum metastability
• Computational complexity of the landscape II - Cosmological considerations
• On Thermalization in de Sitter Space
• The Self-Organized Critical Multiverse
• Lorentzian Vacuum Transitions: Open or Closed Universes?
• Fast optimization algorithms and the cosmological constant
• The Thin-Wall Approximation in Vacuum Decay: a Lemma
• A Stringy Mechanism for A Small Cosmological Constant
• A Stringy Mechanism for A Small Cosmological Constant - Multi-Moduli Cases -
• Anthropic prediction in a large toy landscape
• Search Optimization, Funnel Topography, and Dynamical Criticality on the String Landscape
• Quantum Transitions Between Minkowski and de Sitter Spacetimes
• Accessibility Measure for Eternal Inflation: Dynamical Criticality and Higgs Metastability
• Preference for a Vanishingly Small Cosmological Constant in Supersymmetric Vacua in a Type IIB String Theory Model
• Patient Observers and Non-perturbative Infrared Dynamics in Inflation
• Multitarget search on complex networks: A logarithmic growth of global mean random cover time
• Linking Light Scalar Modes with A Small Positive Cosmological Constant in String Theory
• Statistical Distribution of the Vacuum Energy Density in Racetrack Kähler Uplift Models in String Theory

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• Gauge hierarchy from electroweak vacuum metastability
• Gravity-improved metastability bounds for the Type-I Seesaw Mechanism
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• Hubble selection of the weak scale from QCD quantum critical point
• Hierarchies from Landscape Probability Gradients and Critical Boundaries
• Gauge hierarchy and metastability from Higgs-driven crunching