标题： 二阶协变不变宇宙学扰动理论：-- 用协变不变变量表示的爱因斯坦方程 -- 显示英文标题

标题： Second-order Gauge Invariant Cosmological Perturbation Theory: -- Einstein equations in terms of gauge invariant variables --

摘要： 在论文[K. Nakamura, Prog. Theor. Phys.{\bf 110}(2003), 723;{\it 同上},{\bf 113}(2005), 481.]中发展出的规范不变扰动理论的一般框架下，我们在四维均匀各向同性宇宙中建立了二阶规范不变的宇宙学扰动理论。我们考虑了由单一完美流体主导的宇宙和由单一标量场主导的宇宙中的扰动。我们推导了当一阶矢量和张量模式可以忽略时爱因斯坦方程的所有分量。所有方程都是用规范不变变量推导出来的，不需要任何规范选取。这些方程表明，二阶矢量和张量模式可能是由于一阶标量扰动的模态耦合而产生的。我们还通过与一些文献的比较简要讨论了本工作的主要进展。 显示英文摘要

摘要： Along the general framework of the gauge invariant perturbation theory developed in the papers [K. Nakamura, Prog. Theor. Phys. {\bf 110} (2003), 723; {\it ibid}, {\bf 113} (2005), 481.], we formulate the second order gauge invariant cosmological perturbation theory in a four dimensional homogeneous isotropic universe. We consider the perturbations both in the universe dominated by the single perfect fluid and in that dominated by the single scalar field. We derive the all components of the Einstein equations in the case where the first order vector and tensor modes are negligible. All equations are derived in terms of gauge invariant variables without any gauge fixing. These equations imply that the second order vector and tensor modes may be generated due to the mode-mode coupling of the linear order scalar perturbations. We also briefly discuss the main progress of this work by the comparison with some literatures.