Eternal Inflation in 3D: Pocket Universes

Eternal Inflation · 3D

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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Volume covered

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Our bubble age

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How it works

Same eternal-inflation mechanism as the 2D diagram, but simulated through an actual comoving 3D volume instead of a flat slice. Bubbles of true vacuum nucleate at random 3D points inside a false-vacuum background expanding as a(t) = e^Ht, following a Poisson process with rate λ per unit comoving volume per unit time. Each bubble's wall races outward near light-speed, but its comoving radius saturates because the background keeps stretching space faster than the wall can cross it.

a(t) = e^(H·t)
R_comoving(t) = (c_wall/H)·(1 − e^(−H·(t−t_nuc)))
one gold sphere = "our" pocket universe, picked at nucleation

Nucleation rate λ — spawn rate of new spheres throughout the volume, not just on a plane; a 3D count grows with the cube of reach, so the multiverse fills out far faster than the flat picture suggests.
Hubble rate H — sets each bubble's saturation radius c_wall/H in every direction at once; raise it and inflation outruns the walls in all three dimensions simultaneously.
Wall speed — physical propagation speed of the true-vacuum boundary, capped below c.
Domain walls — where two spheres genuinely intersect in 3D, the overlap is rendered as an oriented ring at the true intersection circle of the two spheres — the actual 3D domain-wall geometry, not a projected line.

Orbit the camera to see that collisions are not confined to a plane: a companion bubble can approach from any direction in the volume, which is why a real bubble-collision signature in the CMB would appear as a disk on our sky rather than a point — we only ever see the 2D slice where another bubble's 3D wall crosses our own.

Pocket universe (bubble) Our universe Domain-wall ring

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