论文标题
带有完美流体的重力标量扰动的二阶有效摩托张量
Second-order effective energy-momentum tensor of gravitational scalar perturbations with perfect fluid
论文作者
论文摘要
我们研究了压缩流体的二阶重力标量扰动。我们得出了由重力和物质扰动的二次术语描述的有效能量张量。我们表明，二阶有效能量量张量取决于仪表。我们施加了三个量规条件（纵向，空间式和仪表仪），以进行灰尘和辐射。所得的能量量张量仅通过规格不变变量来描述，但功能形式取决于量规选择。在具有类似粉尘的流体背景的物质主导的时期中，二阶有效能量密度和扰动的压力在所有三个量规选择中以1/a^2的形式演变为1/a^2，例如宇宙的曲率密度，但它们没有提供正确的状态方程。该参数的值也取决于量规选择。在辐射主导的时期中，短波极限的扰动的表现与纵向和空间上的仪表中的辐射样流体相同。但是，它们在共同的仪表中以不同的方式行事。总体而言，我们得出的结论是，标量扰动的二阶有效能量张量严格取决于计量。
We investigate the second-order gravitational scalar perturbations for a barotropic fluid. We derive the effective energy-momentum tensor described by the quadratic terms of the gravitational and the matter perturbations. We show that the second-order effective energy-momentum tensor is gauge dependent. We impose three gauge conditions (longitudinal, spatially-flat, and comoving gauges) for dust and radiation. The resulting energy-momentum tensor is described only by a gauge invariant variable, but the functional form depends on the gauge choice. In the matter-dominated epoch with dust-like fluid background, the second-order effective energy density and pressure of the perturbations evolve as 1/a^2 in all three gauge choices, like the curvature density of the Universe, but they do not provide the correct equation of state. The value of this parameter depends also on the gauge choice. In the radiation-dominated epoch, the perturbations in the short-wave limit behave in the same way as the radiation-like fluid in the longitudinal and the spatially-flat gauges. However, they behave in a different way in the comoving gauge. As a whole, we conclude that the second-order effective energy-momentum tensor of the scalar perturbation is strictly gauge dependent.
