False Vacuum Decay: Bubble Nucleation

Potential Shape

Vacuum energy split ε 1.00

Wall tension σ 1.00

Attempt prefactor A 1.0×10⁻²

Wall speed (×c) 0.60

Live Readouts

Bounce action B

—

Nucleation rate Γ/cell

—

Bubbles nucleated

True-vacuum fraction

0.0%

Critical radius ρ_c

—

Elapsed time

0.0 s

How it works

The lattice is a scalar field φ sitting in a potential with two unequal minima: a metastable false vacuum (blue, higher energy) and a true, lower-energy vacuum (orange), separated by a barrier of surface tension σ. Classically the field is stuck — it can only escape by quantum tunnelling through the barrier, nucleating a bubble of true vacuum.

Coleman's thin-wall (O(4)-symmetric) instanton gives the tunnelling exponent and the size of the critical bubble in terms of the vacuum energy difference ε and the wall tension σ:

B = 27π²σ⁴ / (2ε³)        (Euclidean bounce action)
Γ/V  = A · e^(−B)          (nucleation rate per unit 4-volume)
ρ_c  = 3σ / ε              (critical bubble radius)

A bubble smaller than ρ_c would cost more wall energy than it gains from the volume converted, so it re-collapses; a bubble that reaches ρ_c is energetically favoured to keep growing, and its wall runs away toward the speed of light, releasing the latent heat ε per unit volume as it sweeps through the false vacuum.

ε — deepens the true vacuum: lowers B exponentially (rate rises fast) and shrinks ρ_c.
σ — raises the wall's surface energy: increases B (rate falls) and grows ρ_c.
A — the dimensionful tunnelling prefactor; scales how often the lattice attempts a nucleation independent of the exponent.
Wall speed — how fast a nucleated bubble's boundary sweeps outward once past ρ_c.
Bubbles that collide simply merge — once two walls touch, both regions stay converted.

This is the mechanism believed to have ended cosmic inflation (reheating), and — if our own electroweak vacuum turns out to be metastable — the same process, on cosmological timescales, that could one day nucleate a bubble of true vacuum in our universe.

False vacuum True vacuum Bubble wall (active front)

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.