Classical Noise in Transient USR Inflation

Abstract

In single-field inflation, linear perturbations originate as quantum fluctuations and undergo a quantum-to-classical transition on super-horizon scales as the decaying mode of the comoving curvature perturbation ℛ is suppressed. This transition provides a condition for the validity of a classical stochastic description of ℛ. We characterize classicality through the suppression of the quantum commutator relative to phase-space variances and the evolution of the squeezing parameters. In the Starobinsky model, we show that this transition becomes mode-dependent at linear order due to the transient ultra-slow-roll (USR) phase. This is because the decaying mode transiently grows during the USR phase modifying the squeezing dynamics, and shifting the classicalization time depending on when modes exit the horizon relative to the USR phase. We then study the implications of this mode-dependent transition for the stochastic description of perturbations. Using the Green's function method, we show that the stochastic spectrum reproduces the power spectrum of the quantum state initialized in the Bunch-Davies vacuum, independently of the mode-dependent transition when the gradient term is retained in the Langevin equation, for both white and colored noise coarse-graining. In contrast, ignoring the gradient term in the Langevin equation introduces an explicit dependence on the coarse-graining parameter σ. Homogeneous matching procedure can be used to set mode-dependent σ(k) that reproduces the power spectrum of the quantum state at the end of inflation. Crucially, however, we show that the matching times precede the classicalization times for modes near the USR transition. Therefore, the transient USR phase in this model leads to a mode-dependent condition for when linear curvature perturbations can be described as classical stochastic noise.

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Cite

BibTeX RIS

BibTeX

@misc{d2026classical,
  title = {{Classical Noise in Transient USR Inflation}},
  author = {Harish D. N. and Chen-Pin Yeh and Da-Shin Lee},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19478},
  eprint = {2609.19478},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19478},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Classical Noise in Transient USR Inflation
AU  - Harish D. N.
AU  - Chen-Pin Yeh
AU  - Da-Shin Lee
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.19478
UR  - https://arxiv.org/abs/2609.19478
AB  - In single-field inflation, linear perturbations originate as quantum fluctuations and undergo a quantum-to-classical transition on super-horizon scales as the decaying mode of the comoving curvature perturbation ℛ is suppressed. This transition provides a condition for the validity of a classical stochastic description of ℛ. We characterize classicality through the suppression of the quantum commutator relative to phase-space variances and the evolution of the squeezing parameters. In the Starobinsky model, we show that this transition becomes mode-dependent at linear order due to the transient ultra-slow-roll (USR) phase. This is because the decaying mode transiently grows during the USR phase modifying the squeezing dynamics, and shifting the classicalization time depending on when modes exit the horizon relative to the USR phase. We then study the implications of this mode-dependent transition for the stochastic description of perturbations. Using the Green's function method, we show that the stochastic spectrum reproduces the power spectrum of the quantum state initialized in the Bunch-Davies vacuum, independently of the mode-dependent transition when the gradient term is retained in the Langevin equation, for both white and colored noise coarse-graining. In contrast, ignoring the gradient term in the Langevin equation introduces an explicit dependence on the coarse-graining parameter σ. Homogeneous matching procedure can be used to set mode-dependent σ(k) that reproduces the power spectrum of the quantum state at the end of inflation. Crucially, however, we show that the matching times precede the classicalization times for modes near the USR transition. Therefore, the transient USR phase in this model leads to a mode-dependent condition for when linear curvature perturbations can be described as classical stochastic noise.
ER  -

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