AI 中文总结
该研究在哈密顿框架下首次计算多场暴胀二阶微扰的大尺度规范不变相空间变量，推导了相关哈密顿量，其结果与拉格朗日方法文献一致，还给出了高阶微扰的程序概述。
AI 中文摘要
广义相对论与多个标量场耦合是一个微分同胚不变的约束系统。因此，对微扰自由度的朴素计数会不可避免地高估理论中传播的物理模式的真实数量，因为规范冗余和约束方程会移除非动力学模式。虽然线性涨落的这一问题已得到解决，但本工作首次在哈密顿框架下，计算了多场暴胀中所有大尺度规范不变相空间变量在微扰理论二阶下的显式结果。基于著名的Sasaki-Mukhanov变量，我们展示了如何构建一个有限维的二次修正基，该基在规范变换下保持不变。尽管我们的方法对任意数量的场和任意尺度都具有通用性，但为了显式求解，我们将范围限制在超哈勃尺度上，并给出了相应的结果。由此，我们证明可以将通常的平坦规范和共动规范涨落恢复为大尺度规范不变组合，这为连接视界以上的理论预测与观测结果的规范固定程序提供了可靠的一致性检验。我们以与规范无关的方式推导了多场暴胀的二次和三次哈密顿量，随后通过进入平坦规范对理论进行规范固定，并表明其与通常基于拉格朗日方法的相关文献完全一致。在这些具体步骤之后，我们提出了二次阶规范不变变量存在性的更形式化证明，并给出了可将微扰理论推进到更高阶的程序概述。
英文摘要
General relativity coupled to multiple scalar fields is a diffeomorphism-invariant constrained system. Consequently, a naive counting of the perturbative degrees of freedom unavoidably overestimates the true number of physical modes propagating in the theory, as gauge redundancies and constraint equations remove non-dynamical ones. While this problem has been solved for linear fluctuations, this work presents the first explicit calculation of all large-scale gauge-invariant phase-space variables in multifield inflation and at second order in perturbation theory, in a Hamiltonian language. Building upon the well-known Sasaki-Mukhanov variables, we show how to construct a finite-dimensional basis of quadratic corrections which are invariant under gauge transformations. Although our procedure is generic to any number of fields and at any scale, we restrict to super-Hubble scales for their explicit solution, which we deliver. Henceforth, we prove that it is possible to recover the usual flat-gauge and comoving-gauge fluctuations as large-scale gauge-invariant combinations, making for a robust consistency check of the gauge-fixed procedure to connect theoretical predictions above the horizon to observations. We derive the quadratic and cubic Hamiltonian of multifield inflation in a gauge independent manner, then we gauge fix our theory by going into the flat gauge, and we show perfect agreement with the literature on this topic, usually based on a Lagrangian approach. After these concrete steps, we propose a more formal proof of the existence of gauge-invariant variables at quadratic order, and we provide a sketch of the procedure that should allow to go to higher orders in perturbation theory.
Comments34 pages, 10 pages of appendices
