The local competition
During one Hubble time a light scalar field acquires quantum fluctuations of characteristic size roughly H/2π. At the same time the background field classically rolls down its potential. If upward fluctuations are large enough in some regions, those regions can remain at high potential energy while others roll toward the end of inflation.
What self-reproduction means
Because inflating regions expand rapidly, the physical volume still undergoing inflation can continue to grow even while some patches exit inflation and reheat. Repetition of that process creates a branching global structure: local hot universes appear inside a larger spacetime in which inflation continues elsewhere.
Why this is not automatic
Inflation does not imply eternal inflation in every model. The result depends on the potential, field range, quantum diffusion, gravitational backreaction and how one defines the stochastic regime. A model must be examined, not simply labelled “inflationary.”
The measure problem
If a global eternally inflating spacetime produces arbitrarily large numbers of regions, ordinary frequency counting becomes ambiguous. Probabilities depend on how the infinite spacetime is regulated. This “measure problem” is one reason multiverse predictions are difficult even when the underlying dynamics are specified.
Observational status
No pocket universe has been directly observed. Proposed signatures such as bubble collisions are model specific and difficult to distinguish from statistical anomalies or foregrounds. Eternal inflation therefore remains a theoretically motivated, model-dependent extension rather than an established observational fact.