Stochastic Inflation with Interacting Noises

2025/08/13 by Nassiri-Rad, Amin, Sheikhahmadi, Haidar, Firouzjahi, Hassan · 2 citations
#Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2508.09946

Abstract

Stochastic δN formalism is a powerful tool to calculate the cosmological correlators non-perturbatively. However, it requires the initial data for the amplitude of the noise on the initial flat hypersurface which for a free theory during inflation is fixed to be (H)/(2 π). In this work, we study the setups where the underlying theory involves interactions and the stochastic noises inherit these interactions. We extend the stochastic δN formalism to these setups and rewrite the corresponding Langevin and Fokker-Planck equations in which the QFT corrections in the amplitude of the noises are taken into account. As an example, in the three-phase SR-USR-SR setup which is employed for PBHs formation, the modification in the amplitude of noise is calculated from the one-loop corrections in power spectrum via in-in formalism. We show that in these setups the amplitude of the stochastic noise is modified to (H)/(2 π) (1+ \frac Δ\cal P_{\cal R} \cal P⁽⁰⁾_ \cal R )^(1)/(2) in which \fracΔ\cal P_{\cal R} \cal P⁽⁰⁾_\cal R is the fractional one-loop correction in power spectrum.

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Cited by

• Trispectrum in Extended USR Model with Transition to SR
• Stochastic inflation with gradient interactions

Related

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• Small noise expansion of stochastic inflation
• Stochastic instantons and the tail of the inflationary density perturbation
• Recent Developments in Stochastic Inflation
• Stochastic origin of primordial fluctuations in the Sky