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arXiv 2201.10333hep-thgr-qc
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暴胀引起的引力波的随机逼近

Stochastic approach to gravitational waves from inflation

Gianmassimo Tasinato

摘要:

我们提出了一个粗粒化的过程来描述暴胀张量模的超视界动力学。我们的目标是制定一个随机描述的自旋2模式的统计种子的背景下,引力波从通货膨胀。利用量子力学的基本原理,我们确定了粗粒张量场的概率密度,它满足超视界尺度下的随机Fokker-Planck方程。相应的噪声和漂移是可计算的,并且取决于所考虑的宇宙学系统。我们的一般公式适用于各种宇宙学的情况下,也考虑很少考虑的情况下,随机通货膨胀,这是重要的观测结果。我们开始获得预期的表达式,噪声和漂移在纯德西特和幂律膨胀,还包括非吸引子阶段的影响的讨论。然后,我们应用我们的方法来描述从暴胀过渡到辐射和物质主导的标准宇宙学时代的场景。我们展示了如何通过宇宙视界流动的模式之间的干扰,以及在超视界尺度自发产生的模式,可以影响粗粒度张量的随机演化。在适当的限制,我们发现,相应的频谱张量模式在视界交叉匹配的结果,量子场论计算,但我们也强调的差异可能会出现。

英文摘要:

We propose a coarse-graining procedure for describing the superhorizon dynamics of inflationary tensor modes. Our aim is to formulate a stochastic description for the statistics of spin-2 modes which seed the background of gravitational waves from inflation. Using basic principles of quantum mechanics, we determine a probability density for coarse-grained tensor fields, which satisfies a stochastic Fokker-Planck equation at superhorizon scales. The corresponding noise and drift are computable, and depend on the cosmological system under consideration. Our general formulas are applied to a variety of cosmological scenarios, also considering cases seldom considered in the context of stochastic inflation, and which are important for their observational consequences. We start obtaining the expected expressions for noise and drift in pure de Sitter and power-law inflation, also including a discussion of effects of non-attractor phases. We then apply our methods to describe scenarios with a transition from inflation to standard cosmological eras of radiation and matter domination. We show how the interference between modes flowing through the cosmological horizon, and modes spontaneously produced at superhorizon scales, can affect the stochastic evolution of coarse-grained tensor quantities. In appropriate limits, we find that the corresponding spectrum of tensor modes at horizon crossing matches with the results of quantum field theory calculations, but we also highlight where differences can arise.

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