基于施温格-凯尔迪什形式主义的宇宙学真空衰变
Cosmological Vacuum Decays from Schwinger-Keldysh Formalism
AI总结：
本研究基于施温格-凯尔迪什形式主义建立框架，通过分解相变场得到平均场的朗之万型运动方程，以多项式势为例分析相关结构，为数值模拟宇宙学一阶相变动力学提供基础。
AI中文摘要：
在本研究中，我们建立了一套系统框架，用于描述辐射主导的FLRW宇宙中基于施温格-凯尔迪什（Schwinger-Keldysh）形式主义的真空衰变。通过将相变场Φ分解为平均场φ和短波长模式σ，并将后者作为环境求迹，我们得到了平均场φ的经典朗之万型运动方程，其中量子效应编码在非马尔可夫记忆核和非高斯噪声中。作为一个唯象例子，我们考虑多项式势并研究记忆核的结构以及噪声项的关联函数。通过允许φ携带空间依赖的更宽松尺度划分，未来可进一步扩展，通过数值模拟描述宇宙学一阶相变的完整动力学。
英文摘要：
In this work, we establish a systematic framework to describe the vacuum decays in a radiation-dominated FLRW universe from the Schwinger-Keldysh formalism. By splitting the phase transition field $Φ$ into the mean field $ϕ$ and the short-wavelength modes $σ$ and tracing over the latter as the environment, we obtain a classical Langevin-type equation-of-motion for the mean field $ϕ$, where the quantum effects are encoded in a non-Markov memory kernel and a non-Gaussian noise. As a phenomenological example, we consider a polynomial potential and study the structure of the memory kernel as well as the correlation functions of the noise term. With a less restrictive scale split by allowing $ϕ$ to carry spatial dependence, further extensions remain possible to describe the whole dynamics of cosmological first-order phase transitions via numerical simulations.
