标题： 宇宙学扰动理论在同步规范与共形牛顿规范中的比较 显示英文标题

标题： Cosmological Perturbation Theory in the Synchronous vs. Conformal Newtonian Gauge

摘要： 我们系统地处理了同步规范和共形牛顿（或纵向）规范中标量引力扰动的线性理论。 我们首先推导出两个规范之间的变换规律。 然后在两个规范中同时写出耦合的、线性化的玻尔兹曼方程、爱因斯坦方程和流体方程，这些方程描述了度规扰动和粒子种类密度波动的演化。 所考虑的粒子种类包括冷暗物质（CDM）、重子、光子、无质量中微子和有质量中微子（一种热暗物质或HDM候选者），其中CDM和重子组分被当作流体处理，而对光子和中微子则给出了详细的相空间描述。 所提出的线性演化方程适用于任何包含CDM或CDM与HDM混合的$\Omega=1$模型。 得到了超视界尺度上的等熵初始条件。 对于具有$\Omega_{\rm cold}=0.65,$$\Omega_{\rm hot}=0.3$和$\Omega_{\rm baryon}=0.05$的CDM+HDM模型，这两个规范中的方程被数值求解。 我们讨论了度规和密度扰动的演化，并比较了在两个规范中视界外的不同行为。 在一篇配套论文中，我们在此处计算的扰动共形牛顿背景度规中积分中微子粒子的测地线方程。 目的是为了在CDM+HDM模型的$N$-体模拟中，对HDM初始条件下的中微子相空间进行精确采样。 显示英文摘要

摘要： We present a systematic treatment of the linear theory of scalar gravitational perturbations in the synchronous gauge and the conformal Newtonian (or longitudinal) gauge. We first derive the transformation law relating the two gauges. We then write down in parallel in both gauges the coupled, linearized Boltzmann, Einstein and fluid equations that govern the evolution of the metric perturbations and the density fluctuations of the particle species. The particle species considered include cold dark matter (CDM), baryons, photons, massless neutrinos, and massive neutrinos (a hot dark matter or HDM candidate), where the CDM and baryon components are treated as fluids while a detailed phase-space description is given to the photons and neutrinos. The linear evolution equations presented are applicable to any $\Omega=1$ model with CDM or a mixture of CDM and HDM. Isentropic initial conditions on super-horizon scales are derived. The equations are solved numerically in both gauges for a CDM+HDM model with $\Omega_{\rm cold}=0.65,$ $\Omega_{\rm hot}=0.3$, and $\Omega_{\rm baryon}=0.05$. We discuss the evolution of the metric and the density perturbations and compare their different behaviors outside the horizon in the two gauges. In a companion paper we integrate the geodesic equations for the neutrino particles in the perturbed conformal Newtonian background metric computed here. The purpose is to obtain an accurate sampling of the neutrino phase space for the HDM initial conditions in $N$-body simulations of the CDM+HDM models.