Eternal Inflation: Bubble Nucleation

Eternal Inflation

Nucleation rate λ 0.35

Hubble rate H 1.0

Wall speed (×c) 1.0

Bubbles nucleated

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Collisions

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Area covered

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Sim time

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How it works

The background is a false-vacuum spacetime expanding exponentially, scale factor a(t) = e^Ht. Bubbles of true vacuum nucleate at random comoving points with rate λ per unit comoving area per unit time — a Poisson process, following the Coleman–De Luccia instanton picture. Once nucleated, a bubble wall moves outward at close to the speed of light in physical coordinates, but because the background keeps stretching space between nucleation and now, its comoving radius does not grow forever — it saturates.

a(t) = e^(H·t)
R_comoving(t) = (c_wall/H)·(1 − e^(−H·(t−t_nuc)))
λ = nucleation rate per comoving area per unit time

Nucleation rate λ — how often new pocket universes pop into existence; higher λ packs more bubbles into the same comoving volume before they saturate.
Hubble rate H — the false vacuum's expansion rate. A larger H caps each bubble's comoving reach at c_wall/H, so faster inflation outruns the bubble walls and space is never fully converted — the "graceful exit" problem that makes inflation eternal.
Wall speed — how close to light-speed the true-vacuum wall propagates; slower walls saturate to a smaller radius for the same H.
Domain walls — when two bubble walls meet, they don't merge; the collision imprints a scar (a domain wall) at the overlap, one of the few theoretically predicted, in-principle-observable signatures of a companion pocket universe, potentially visible as a disk-shaped anomaly in the CMB.

This is the actual mechanism behind the inflationary multiverse described in Exploring the Multiverse: inflation never fully stops everywhere at once, so it produces an unbounded, ever-growing number of causally disconnected pocket universes — our observable universe would be just one bubble among them.

Pocket universe (bubble) Newest bubble Collision scar