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arXiv 1402.2464astro-ph.CO
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尘埃宇宙学的二阶密度微扰

Second order density perturbations for dust cosmologies

Claes Uggla, John Wainwright

摘要:

我们提出了简单的表达式相对论的一阶和二阶分数密度扰动FL宇宙学的灰尘,在四个不同的规范:泊松,均匀曲率,总物质和同步规范。我们在背景中加入了一个宇宙学常数和任意的空间曲率。我们的方法的一个显着特点是我们的描述的空间依赖性的扰动使用一套规范的二次微分表达式,涉及一个任意的空间函数,产生作为一个保守的数量。这使我们能够统一、简化和扩展之前看似不同的结果。我们使用的原始物质和度量扰动,出现在年底的暴胀时代,以确定额外的任意空间函数时,集成的二阶扰动方程。这将非高斯参数引入到二阶密度扰动的表达式中。在零空间曲率的特殊情况下,我们表明,时间演化简化显着,只需要使用两个非初等函数,所谓的增长抑制因子在线性水平,和一个新的功能在二阶水平。我们期望这些结果在应用上是有用的,例如,研究原始非高斯性对宇宙大尺度结构的影响。

英文摘要:

We present simple expressions for the relativistic first and second order fractional density perturbations for FL cosmologies with dust, in four different gauges: the Poisson, uniform curvature, total matter and synchronous gauges. We include a cosmological constant and arbitrary spatial curvature in the background. A distinctive feature of our approach is our description of the spatial dependence of the perturbations using a canonical set of quadratic differential expressions involving an arbitrary spatial function that arises as a conserved quantity. This enables us to unify, simplify and extend previous seemingly disparate results. We use the primordial matter and metric perturbations that emerge at the end of the inflationary epoch to determine the additional arbitrary spatial function that arises when integrating the second order perturbation equations. This introduces a non-Gaussianity parameter into the expressions for the second order density perturbation. In the special case of zero spatial curvature we show that the time evolution simplifies significantly, and requires the use of only two non-elementary functions, the so-called growth supression factor at the linear level, and one new function at the second order level. We expect that the results will be useful in applications, for example, studying the effects of primordial non-Gaussianity on the large scale structure of the universe.

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