Stochastic Inflation with Interacting Noises
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arXiv
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| Natura: | Preprint |
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2025
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| _version_ | 1866917435276263424 |
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| author | Nassiri-Rad, Amin Sheikhahmadi, Haidar Firouzjahi, Hassan |
| author_facet | Nassiri-Rad, Amin Sheikhahmadi, Haidar Firouzjahi, Hassan |
| contents | 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 $\frac{H}{2 π}$. 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 $\frac{H}{2 π} \Big(1+ \frac{ Δ{\cal P}_{\cal R} }{ {\cal P}^{(0)}_{ {\cal R} } }\Big)^{\frac{1}{2}}$ in which $ \frac{Δ{\cal P}_{\cal R} }{ {\cal P}^{(0)}_{{\cal R} } }$ is the fractional one-loop correction in power spectrum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09946 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stochastic Inflation with Interacting Noises Nassiri-Rad, Amin Sheikhahmadi, Haidar Firouzjahi, Hassan Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology High Energy Physics - Theory 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 $\frac{H}{2 π}$. 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 $\frac{H}{2 π} \Big(1+ \frac{ Δ{\cal P}_{\cal R} }{ {\cal P}^{(0)}_{ {\cal R} } }\Big)^{\frac{1}{2}}$ in which $ \frac{Δ{\cal P}_{\cal R} }{ {\cal P}^{(0)}_{{\cal R} } }$ is the fractional one-loop correction in power spectrum. |
| title | Stochastic Inflation with Interacting Noises |
| topic | Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2508.09946 |