瞬态超慢滚暴涨中的经典噪声
Classical Noise in Transient USR Inflation
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中文总结 AI 辅助
该研究在Starobinsky模型中揭示瞬态超慢滚阶段使曲率扰动的量子-经典转变依赖于模式，并分析其对随机描述的影响，发现保留梯度项的Langevin方程可重现量子功率谱，但匹配时间早于经典化时间。
中文摘要 AI 辅助
在单场暴涨中，线性扰动起源于量子涨落，并在超视界尺度上经历从量子到经典的转变，这一转变伴随着共动曲率扰动 $\mathcal{R}$ 的衰减模被抑制。该转变为 $\mathcal{R}$ 的经典随机描述的有效性提供了条件。我们通过量子对易子相对于相空间方差的抑制以及挤压参数的演化来刻画经典性。在 Starobinsky 模型中，我们证明由于瞬态超慢滚（USR）阶段的存在，该转变在线性阶上变得依赖于模式。这是因为在 USR 阶段，衰减模会瞬态增长，从而改变挤压动力学，并根据模式相对于 USR 阶段退出视界的时间而改变经典化时间。随后，我们研究了这种依赖于模式的转变对扰动随机描述的影响。利用格林函数方法，我们证明当在 Langevin 方程中保留梯度项时，对于白噪声和有色噪声的粗粒化，随机谱都能重现初始化为 Bunch-Davies 真空的量子态的功率谱，且与依赖于模式的转变无关。相反，忽略 Langevin 方程中的梯度项会引入对粗粒化参数 $\sigma$ 的显式依赖。可以采用齐次匹配程序来设置依赖于模式的 $\sigma(k)$，从而在暴涨结束时重现量子态的功率谱。然而，至关重要的是，我们证明对于接近 USR 转变的模式，匹配时间早于经典化时间。因此，该模型中的瞬态 USR 阶段为线性曲率扰动何时可被描述为经典随机噪声提供了依赖于模式的条件。
英文摘要
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 $\mathcal{R}$ is suppressed. This transition provides a condition for the validity of a classical stochastic description of $\mathcal{R}$. 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.
发表机构
- National Dong Hwa University（东华大学）
- National Center for Theoretical Sciences（国家理论科学中心）
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