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Absolute Lower Bound on the Bounce Action.

Ryosuke Sato1, Masahiro Takimoto1,2

  • 1Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 7610001, Israel.

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|March 17, 2018
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Researchers derived a lower bound for the bounce action, crucial for understanding false vacuum decay rates. This provides a simple, sufficient condition for vacuum stability in scalar field models.

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Area of Science:

  • * Theoretical Physics
  • * Cosmology
  • * Quantum Field Theory

Background:

  • * The decay rate of a false vacuum is governed by the minimal action solution of the tunneling field, known as the bounce.
  • * Understanding vacuum stability is critical in cosmology and particle physics.

Purpose of the Study:

  • * To derive an absolute lower bound on the bounce action for scalar fields in N(>2) dimensional Euclidean space.
  • * To establish a sufficient condition for false vacuum stability without explicitly solving equations of motion.

Main Methods:

  • * Focus on scalar field models with canonical kinetic terms.
  • * Derive a lower bound on the bounce action using a simplified analytical approach.
  • * Analyze the four-dimensional case to establish a specific bound related to the potential V(ϕ).

Main Results:

  • * An absolute lower bound on the bounce action was derived for scalar field models.
  • * In four dimensions, the bounce action is shown to be generically larger than 24/λ_{cr}.
  • * The derived bound serves as a sufficient condition for vacuum stability and is applicable to various scalar potentials and fields.

Conclusions:

  • * The study provides a simple yet powerful tool for assessing vacuum stability.
  • * The derived bound is broadly applicable and useful even when explicit bounce solutions are intractable.
  • * A necessary condition for the bounce action approaching the lower bound was also discussed.