Stochastic Inflation Dynamics in Cosmological Models

Inflationary cosmology posits a brief epoch of accelerated expansion driven by one or more scalar fields. In realistic scenarios, quantum fluctuations on super-Hubble scales accumulate and induce stochastic behaviour of the inflaton field, modifying predictions for primordial density perturbations. The stochastic inflation framework treats the long-wavelength component of the inflaton as a classical random variable subject to a Langevin equation, with a noise term encoding the continuous inflow of quantum fluctuations. Its equivalent Fokker-Planck description yields a probability distribution for field values and hence for the number of e-folds of expansion. This approach captures non-perturbative effects, such as rare large fluctuations that can seed primordial black holes or generate non-Gaussian tails in the curvature perturbation. Modern developments have clarified the link between the underlying quantum field theory and the stochastic formalism via renormalisation-group methods, and have extended the treatment to multi-field and non-canonical models. Applications span predictions for cosmic microwave background observables, the abundance of early universe relics and the global structure of the inflating spacetime, including regimes of eternal inflation where stochastic noise dominates the classical roll of the field.

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Stochastic Inflation Dynamics in Cosmological Models publication trend

The graph below shows the total number of articles in stochastic inflation dynamics in cosmological models across all publications each year (not limited to Nature Index journals).

Technical terms

Stochastic inflation: A description of long-wavelength inflaton dynamics as a classical random process driven by quantum noise.

Langevin equation: A differential equation for a system’s evolution including a deterministic drift and a stochastic noise term.

Fokker-Planck equation: A partial differential equation governing the time evolution of a probability distribution under drift and diffusion.

Separate-universe approach: An approximation treating each super-Hubble region as an independent homogeneous universe.

δN formalism: A method relating local curvature perturbations to spatial variations in the number of inflationary e-folds.

References

1. The separate-universe approach and sudden transitions during inflation. Journal of Cosmology and Astroparticle Physics (2024).
2. Borel resummation of secular divergences in stochastic inflation. Journal of High Energy Physics (2023).
3. Correlation functions in stochastic inflation. European Physical Journal C (2015).
4. Multiple fields in stochastic inflation. Journal of Cosmology and Astroparticle Physics (2016).
5. One small step for an inflaton, one giant leap for inflation: A novel non-Gaussian tail and primordial black holes. Physics Letters B (2022).