EFT beyond the horizon: stochastic inflation and how primordial quantum fluctuations go classical
EFT beyond the horizon: stochastic inflation and how primordial quantum fluctuations go classical
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DOI：
10.1007/jhep03(2015)090
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发表时间：
2015-03-18
影响因子：
5.4
通讯作者：
Williams, M.
中科院分区：
文献类型：
--
作者：
Burgess, C. P.;Holman, R.;Williams, M.
我们确定了描述超哈勃尺度物理的有效场论，并证明它是一类适用于开放系统的有效场论的特例。开放系统是那些允许在感兴趣的自由度和那些积分出来的自由度之间交换信息的系统，例如适合于粒子在流体中运动的系统。严格地说，它们一般不能用有效的拉格朗日来描述；相反，适当的“低能量”极限是描述慢自由度密度矩阵的时间演化的Lindblad方程。我们导出了与de Sitter(和Near-De-Sitter)时空中量子场的超哈勃模有关的方程，并导出了它的两个含义。结果表明，对角线密度矩阵元的演化迅速逼近Starobinsky随机膨胀图的Fokker-Planck方程。这使我们能够识别主要的修正，并提供这张图片的随机噪声和漂移的替代第一原理推导。(作为应用，我们证明了无质量场的噪声与所用窗函数的细节无关，并且还计算了具有亚光速声速的系统的噪声如何变化，c(S)和lt；1。)然后我们论证了相互作用的存在使场基中的非对角线密度矩阵元素变为零。这就解释了为什么场基通常是当原始量子涨落在视界外时退相干的过程的“指针基”，从而允许它们稍后作为经典的场涨落重新进入，就像分析CMB数据时所假设的那样。退相干过程是非常有效的，即使对于像引力强度这样弱的相互作用，也会在哈勃数次之后发生。重要的是，相互作用的细节在很大程度上只控制了退相干时间，而不是最终的后期随机状态的性质，就像相互作用可以控制热系统的平衡时间一样，但在很大程度上与所产生的平衡态的性质无关。
We identify the effective field theory describing the physics of super-Hubble scales and show it to be a special case of a class of effective field theories appropriate to open systems. Open systems are those that allow information to be exchanged between the degrees of freedom of interest and those that are integrated out, such as would be appropriate for particles moving through a fluid. Strictly speaking they cannot in general be described by an effective lagrangian; rather the appropriate 'low-energy' limit is instead a Lindblad equation describing the time-evolution of the density matrix of the slow degrees of freedom. We derive the equation relevant to super-Hubble modes of quantum fields in de Sitter (and near-de Sitter) spacetimes and derive two of its implications. We show that the evolution of the diagonal density-matrix elements quickly approach the Fokker-Planck equation of Starobinsky's stochastic inflationary picture. This allows us both to identify the leading corrections and provide an alternative first-principles derivation of this picture's stochastic noise and drift. (As applications we show that the noise for massless fields is independent of the details of the window function used, and also compute how the noise changes for systems with a sub-luminal speed of sound, c(s) < 1.) We then argue that the presence of interactions drive the off-diagonal density-matrix elements to zero in the field basis. This shows why the field basis is generally the 'pointer basis' for the process that decoheres primordial quantum fluctuations while they are outside the horizon, thus allowing them to re-enter later as classical field fluctuations, as assumed when analyzing CMB data. The decoherence process is very efficient, occurring after several Hubble times even for interactions as weak as gravitational-strength. Crucially, the details of the interactions largely control only the decoherence time and not the nature of the final late-time stochastic state, much as interactions can control the equilibration time for thermal systems but are largely irrelevant to the properties of the resulting equilibrium state.