Stochastic evolution of scalar fields with continuous symmetries during inflation

Abstract

During inflation, scalar fields with masses less than the Hubble scale acquire vacuum expectation values (vevs) via stochastic processes driven by quantum fluctuations. For nearly massless spectator scalars transforming nontrivially under a continuous symmetry group, we demonstrate that the evolution of the vev depends on the dimensionality of the scalar field space. Fields in larger representations both attain larger vacuum expectation values and converge more rapidly to equilibrium. We present an argument demonstrating how this higher-dimensional evolution can be obtained in unitary gauge for fields transforming under local symmetries with a mass gap that is small compared to the Hubble scale. Finally, we show that accounting for the full number of degrees of freedom in the Standard Model Higgs multiplet tightens Higgs stability constraints on the inflationary scale at the percent level and has more dramatic consequences for both the vev and the energy stored in the Higgs field after inflation.

17 pages, 10 figures Updated to match version accepted by PRD

References in corpus (9)

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• Gravitational corrections to Standard Model vacuum decay
• Higgs Dynamics during Inflation
• Postinflationary Higgs relaxation and the origin of matter-antimatter asymmetry
• Spacetime Dynamics of a Higgs Vacuum Instability During Inflation
• Spectator Dark Matter
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Cited by in corpus (12)

• A manifestly covariant theory of multifield stochastic inflation in phase space: solving the discretisation ambiguity in stochastic inflation
• The Secret Higgstory of the Highest Temperature during Reheating
• Vacuum decay constraints on the Higgs curvature coupling from inflation
• Quintessential Inflation with Dynamical Higgs Generation as an Affine Gravity
• Large Density Perturbations from Reheating to Standard Model particles due to the Dynamics of the Higgs Boson during Inflation
• The $1/N$ expansion for stochastic fields in de Sitter spacetime
• Spectator dark matter in non-standard cosmologies
• Stochastic Baryogenesis
• Primordial non-Gaussianity from the Effects of the Standard Model Higgs during Reheating after Inflation
• Emergent particles of de Sitter: thermal interpretation of the stochastic formalism and beyond
• Probing baryogenesis with gravitational waves
• The effective Higgs potential and vacuum decay in Starobinsky inflation