
A framework that treats the inflaton field's quantum fluctuations as a stochastic process to model inflation.Stochastic inflation is a theoretical framework that describes the behavior of the inflaton field—the field responsible for cosmic inflation—by treating its quantum fluctuations as a classical stochastic (random) process. During inflation, the universe expands exponentially, and quantum fluctuations of the inflaton are stretched to cosmological scales. These fluctuations become the seeds for large-scale structure. The stochastic approach separates the field into a long-wavelength, slowly varying part and short-wavelength fluctuations that act as random kicks, leading to a diffusion-like equation for the field's probability distribution.
The stochastic approach to inflation was developed in the late 1980s by Alexei Starobinsky and, independently, by Andreas Albrecht and Paul Steinhardt, building on earlier work by Vilenkin and others.
The framework splits the inflaton field into a coarse-grained part (averaged over a Hubble volume) and a fluctuating part. The short-wavelength fluctuations are integrated out, leaving a Langevin equation for the coarse-grained field with a noise term. This equation describes how the field undergoes a random walk, with the noise amplitude determined by the Hubble parameter. Solving the associated Fokker-Planck equation gives the probability distribution of the field, which can be used to compute the spectrum of density perturbations and the probability of eternal inflation.
It is used to calculate the primordial power spectrum and to study the possibility of eternal inflation, where inflation never ends globally.
In stochastic inflation, the inflaton field can sometimes fluctuate 'uphill' against its potential, leading to regions where inflation continues indefinitely—a scenario called eternal inflation.









