Adiabatic Modes in Cosmology
Adiabatic Modes in Cosmology
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宇宙学中的绝热模态
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
S. Weinberg
中科院分区：
文献类型：
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作者：
S. Weinberg
我们证明了牛顿规范中的宇宙学扰动场方程总是有一个绝热解，其中一个量$\mathcal{R}$在大波长极限的所有时代都是非零的常数，因此它可以用来将观测到的这种模式下的宇宙学涨落与很早时候的涨落联系起来。还有第二种绝热模式，对于这种模式，$\mathcal{R}$在大波长下消失，通常也可能存在非绝热模式。这些结论适用于所有时代，无论宇宙的成分是什么，只要对大波长场方程的波长依赖做一个温和的技术假设。在没有各向异性惯性的情况下，用Robertson-Walker尺度因子的通用公式给出了大波长绝热模态的微扰。我们讨论了这些结果与在同步规中发现的大波长下所有模态的守恒定律之间的明显差异：事实证明，尽管等效，同步规和牛顿规对大波长下的扰动行为提出了不等价的假设。
We show that the field equations for cosmological perturbations in the Newtonian gauge always have an adiabatic solution, for which a quantity $\mathcal{R}$ is nonzero and constant in all eras in the limit of large wavelength, so that it can be used to connect observed cosmological fluctuations in this mode with those at very early times. There is also a second adiabatic mode, for which $\mathcal{R}$ vanishes for a large wavelength, and in general there may be nonadiabatic modes as well. These conclusions apply in all eras and whatever the constituents of the universe, under only a mild technical assumption about the wavelength dependence of the field equations for a large wavelength. In the absence of anisotropic inertia, the perturbations in the adiabatic modes are given for a large wavelength by universal formulas in terms of the Robertson-Walker scale factor. We discuss an apparent discrepancy between these results and what appears to be a conservation law in all modes found for a large wavelength in the synchronous gauge: it turns out that, although equivalent, the synchronous and Newtonian gauges suggest inequivalent assumptions about the behavior of the perturbations for a large wavelength.