标题： 宇宙扰动的有效速度 显示英文标题

标题： Effective speed of cosmological perturbations

摘要： 我们推导出一个有效方程和作用量，用于共动曲率扰动和引力波（GWs），它依赖于一个与时间、动量和极化相关的有效速度，编码了度规扰动之间或与其他场（例如暗能量和暗物质）相互作用的影响。 标量和张量扰动的有效作用量和方程结构相同，且这些有效作用量可以写为Klein-Gordon作用量的形式，其中定义了一个依赖于有效速度的适当有效度规。 该有效作用量重现了并在扰动高阶上推广了在膨胀和暗能量有效场论中得到的结果，或者在具有多个标量场的系统中的曲率扰动结果，其中有效速度编码了熵和各向异性效应。 对于具有不同于爱因斯坦方程场方程的理论，有效方法也可以通过定义适当的有效能动张量来应用。 作为一个例子，我们表明，在广义相对论中，对于一个最小耦合的标量场，由于作用量中超出二次项的耦合，曲率扰动和引力波的有效速度是频率和极化相关的。 显示英文摘要

摘要： We derive an effective equation and action for comoving curvature perturbations and gravitational waves (GWs) in terms of a time, momentum and polarization dependent effective speed, encoding the effects of the interaction among metric perturbations or with other fields, such as dark energy and dark matter. The structure of the effective actions and equations is the same for scalar and tensor perturbations, and the effective actions can be written as the Klein-Gordon action in terms of an appropriately defined effective metric, dependent on the effective speed. The effective action reproduces, and generalizes to higher order in perturbations, results obtained for GWs in the effective field theory of inflation and dark energy, or for curvature perturbations in systems with multiple scalar fields, encoding in the effective speed the effects of both entropy and anisotropy. The effective approach can also be applied to the solutions of theories with field equations different from the Einstein equations, by defining an appropriate effective energy-momentum tensor. As an example, we show that for a minimally coupled scalar field in general relativity, the effective speeds of curvature perturbations and gravitational waves are frequency and polarization dependent, due to their coupling in the action beyond the quadratic order.