The Stochastic Relaxion

Abstract

We revisit the original proposal of cosmological relaxation of the electroweak scale by Graham, Kaplan and Rajendran in which the Higgs mass is scanned during inflation by an axion field, the relaxion. We investigate the regime where the relaxion is subject to large fluctuations during inflation. The stochastic dynamics of the relaxion is described by means of the Fokker-Planck formalism. We derive a new stopping condition for the relaxion taking into account transitions between the neighboring local minima of its potential. Relaxion fluctuations have important consequences even in the "classical-beats-quantum" regime. We determine that for a large Hubble parameter during inflation, the random walk prevents the relaxion from getting trapped at the first minimum. The relaxion stops much further away, where the potential is less shallow. Interestingly, this essentially jeopardises the "runaway relaxion" threat from finite-density effects, restoring most of the relaxion parameter space. We also explore the "quantum-beats-classical" regime, opening large new regions of parameter space. We investigate the consequences for both the QCD and the non-QCD relaxion. The misalignment of the relaxion due to fluctuations around its local minimum opens new phenomenological opportunities.

arXiv comment35 pages and 16 figures in main text, and 15 pages and 2 figures in appendices

References in corpus (57)

• New Developments in the Casimir Effect
• Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale
• Equilibrium State of a Massless Self-Interacting Scalar Field in the De Sitter Background
• Test of the Equivalence Principle Using a Rotating Torsion Balance
• Cosmological Relaxation of the Electroweak Scale
• From the Big Bang Theory to the Theory of a Stationary Universe
• Long-Lived Particles at the Energy Frontier: The MATHUSLA Physics Case
• Stellar cooling bounds on new light particles: plasma mixing effects
• Cosmological bounds on pseudo Nambu-Goldstone bosons
• Searching for Long-lived Particles: A Compact Detector for Exotics at LHCb
• Probing Light Thermal Dark-Matter With a Higgs Portal Mediator
• MICROSCOPE mission: first constraints on the violation of the weak equivalence principle by a light scalar dilaton
• Light inflaton Hunter's Guide
• The Stochastic Axion Scenario
• Is there a supernova bound on axions?
• The QCD Axion Window and Low Scale Inflation
• Relaxion Stars and their detection via Atomic Physics
• Nnaturalness
• The ALP miracle: unified inflaton and dark matter
• Limits on a CP-violating scalar axion-nucleon interaction
• Stationary Universe
• Phenomenology of relaxion-Higgs mixing
• Dark Higgs Bosons at FASER
• Cosmological Higgs-Axion Interplay for a Naturally Small Electroweak Scale
• Predicting the cosmological constant with the scale-factor cutoff measure
• Large Hierarchies from Attractor Vacua
• Relaxation from particle production
• Do We Live in the Center of the World?
• Cosmic Attractors and Gauge Hierarchy
• The ALP miracle revisited
• The Phase Transition to Eternal Inflation
• Boltzmann babies in the proper time measure
• Coherent relaxion dark matter
• Self-Organised Localisation
• Probing the Relaxed Relaxion at the Luminosity and Precision Frontiers
• Revisiting supernova constraints on a light CP-even scalar
• Detecting Hidden Particles with MATHUSLA
• Constraints on Relaxion Windows
• Inflating to the Weak Scale
• The Selfish Higgs
• Higgs relaxation after inflation
• Improved stellar limits on a light CP-even scalar
• Universality of the Volume Bound in Slow-Roll Eternal Inflation
• Formulating the Kramers problem in field theory
• Sliding Naturalness
• The n2EDM experiment at the Paul Scherrer Institute
• Probing the relaxed relaxion and Higgs-portal with S1 & S2
• Relaxion: A Landscape Without Anthropics
• Relaxion Fluctuations (Self-stopping Relaxion) and Overview of Relaxion Stopping Mechanisms
• Low-Scale D-term Inflation and the Relaxion
• Runaway Relaxion from Finite Density
• Constraints on the relaxion mechanism with strongly interacting vector-fermions
• QCD Axion Window and False Vacuum Higgs Inflation
• Relaxion Dark Matter from Stochastic Misalignment
• The Relaxion Measure Problem
• Gravitational tests of electroweak relaxation
• The effective Higgs potential and vacuum decay in Starobinsky inflation

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