各向异性和非绝热性对共动曲率扰动演化的影响
The effects of anisotropy and non-adiabaticity on the evolution of comoving curvature perturbation
摘要：
在物质场能量动量张量中存在各向异性和非绝热项的情况下，我们导出了曲率扰动在共动时间片$\mathcal{R}_c$上的演化方程。该方程是通过在共动时间切片中处理扰动的爱因斯坦方程得到的。它可以用来研究具有各向异性能量-动量张量的系统的共动曲率扰动的演化，例如在存在向量场的情况下，在存在熵的情况下，例如在多场系统中，或者在修正的引力理论中。作为一个简单的应用，在检验了多场系统的同动时间片与一般均匀场时间片不一致后，我们将该方程用于两个最小耦合标量场的情况，导出了同动时间片上曲率和熵扰动的封闭方程组.
英文摘要：
We derive the equation for the evolution of the curvature perturbation on the comoving time slice, $\mathcal{R}_c$, in the presence of anisotropic and non-adiabatic terms in the energy-momentum tensor of matter fields. The equation is obtained by manipulating the perturbed Einstein's equations in the comoving time slice. It could be used to study the evolution of the comoving curvature perturbations for systems with an anisotropic energy-momentum tensor, such as in the presence of vector fields, in the presence of entropy, such as in a multi-field system, or in modified gravity theories. As a simple application, after checking that the comoving time slice for a multi-field system does not coincide with the uniform field time slice in general, we use the equation in the case of two minimally coupled scalar fields and derive a closed set of equations for the curvature and entropy perturbations on the comoving time slice.
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