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Review on stochastic approach to inflation

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arxiv 2203.13852 v2 pith:F6PCW7O2 submitted 2022-03-25 gr-qc

Diego Cruces This is my paper
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keywords stochasticapproachderivationframeworkinflationreviewappearapplication
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We present a review on the state-of-the-art of the mathematical framework known as stochastic inflation, paying special attention to its derivation and giving references for the readers interested on results coming from the application of the stochastic framework to different inflationary scenarios, especially to those of interest for primordial black hole formation. During the derivation of the stochastic formalism, we will emphasise two aspects in particular: the difference between the separate universe approach and the true long wavelength limit of scalar inhomogeneities and the generically non-Markovian nature of the noises that appear in the stochastic equations.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Confronting infrared divergences in de Sitter: loops, logarithms and the stochastic formalism

    hep-th 2025-07 conditional novelty 7.0 of 10

    The authors show that loop corrections do not alter tree-level time dependence in de Sitter correlators, so secular growth is a regularization artifact, not a physical effect.

  2. Large deviations for halos and voids: beyond perturbative non-gaussianities

    astro-ph.CO 2026-07 conditional novelty 6.0 of 10

    Excursion-set halo and void abundances are derived for exponential-tailed non-Gaussian fluctuations, giving new first-passage-time formulas and a void-size-function series.

  3. Deviations from Gaussian White Noise in Stochastic Inflation

    gr-qc 2025-12 conditional novelty 6.0 of 10

    Relaxing the sharp cutoff or the Bunch-Davies initial state in stochastic inflation makes the noise colored, and relaxing the initial state also makes it non-Gaussian.

  4. An Unfinished Collaboration with A. A. Starobinsky

    gr-qc 2025-08 conditional novelty 6.0 of 10

    Quantum gravitational infrared fluctuations could make the rescaled spatial metric undergo Brownian motion on SL(3,R)/SO(3), producing exponential anisotropy and a quantum violation of cosmic no-hair.

  5. Stochastic inflation as an open quantum system

    hep-th 2025-07 conditional novelty 6.0 of 10

    Stochastic inflation emerges from an open-quantum-system derivation, with a Lindblad master equation that reduces to and corrects Starobinsky's Fokker-Planck equation.

  6. Lectures on Open Systems and Cosmology

    hep-th 2026-07 unverdicted novelty 1.0 of 10

    A pedagogical review that presents the density-matrix/master-equation formalism and the Schwinger–Keldysh path integral in one notation and applies them to inflation; it claims no new result.

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