标题： 明确规范不变的广义相对论微扰理论：II. FRW 背景与一阶微扰 显示英文标题

标题： Manifestly Gauge-Invariant General Relativistic Perturbation Theory: II. FRW Background and First Order

摘要： 在我们的配套论文中，我们确定了广义相对论的一组完整的明显规范不变可观测量。 这是通过将引力和物质系统耦合到无压尘埃中实现的，该尘埃起到了动态耦合观测者的作用。 这些可观测量的演化由一个物理哈密顿量支配，我们推导出了相应的运动方程。 然后，我们在一般精确解的背景下，发展了这些运动方程的线性微扰理论，形式为明显的规范不变微扰。 在本文中，我们将之前的结果专门应用于也是我们修正运动方程解的FRW背景。 然后，我们将由此得到的方程与标准宇宙微扰理论（SCPT）中推导出的方程进行比较。 我们展示了我们显式规范不变微扰与SCPT中的线性规范不变变量之间的精确关系。 我们发现，我们的运动方程可以写成SCPT的形式加上修正项。 这些修正项是以守恒的能量动量流密度形式，在系统中留下的尘埃的痕迹。 结果表明，这些修正项实际上会衰减，在晚期宇宙中，无论守恒流的值如何，它们都是微不足道的。 我们得出结论，添加作为测试观测介质的尘埃虽然暗示爱因斯坦方程在没有尘埃的情况下发生了修改，但与已知结果达成了可接受的吻合，同时具有优势，即我们现在讨论的是显式的规范不变量，即可测量的量，即使在高阶微扰理论中也可以使用。 显示英文摘要

摘要： In our companion paper we identified a complete set of manifestly gauge-invariant observables for general relativity. This was possible by coupling the system of gravity and matter to pressureless dust which plays the role of a dynamically coupled observer. The evolution of those observables is governed by a physical Hamiltonian and we derived the corresponding equations of motion. Linear perturbation theory of those equations of motion around a general exact solution in terms of manifestly gauge invariant perturbations was then developed. In this paper we specialise our previous results to an FRW background which is also a solution of our modified equations of motion. We then compare the resulting equations with those derived in standard cosmological perturbation theory (SCPT). We exhibit the precise relation between our manifestly gauge-invariant perturbations and the linearly gauge-invariant variables in SCPT. We find that our equations of motion can be cast into SCPT form plus corrections. These corrections are the trace that the dust leaves on the system in terms of a conserved energy momentum current density. It turns out that these corrections decay, in fact, in the late universe they are negligible whatever the value of the conserved current. We conclude that the addition of dust which serves as a test observer medium, while implying modifications of Einstein's equations without dust, leads to acceptable agreement with known results, while having the advantage that one now talks about manifestly gauge-invariant, that is measurable, quantities, which can be used even in perturbation theory at higher orders.