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arXiv 1305.0010astro-ph.COgr-qc
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冷暗物质粒子的初始条件与广义相对论

Initial conditions for cold dark matter particles and General Relativity

Cornelius Rampf, Gerasimos Rigopoulos

摘要:

我们用相对论梯度展开描述了宇宙中的无旋尘埃成分,并将由此产生的同步度规转换到牛顿坐标系中。这两个度量通过类空间位移场和类时间扰动连接,提供了从拉格朗日坐标到欧拉坐标的变换的相对论推广。位移场的相对论部分在初始时刻已经产生了二阶非局域密度扰动。这是一个纯粹的相对论效应,因为它起源于时空混合。我们给出了两种选择,被动和主动的方法,如何包括相对论修正,例如在N体模拟。在被动方法中,我们将校正视为初始高斯场的非高斯修改(也可以合并原始非高斯性)。诱导的非高斯性依赖于初始条件的尺度和红移,当尺度和红移足够小时,f_NL ~ few。在主动方法中,我们展示了如何使用相对论轨迹来获得N体模拟的粒子的初始位移和速度,而无需修改初始高斯场。

英文摘要:

We describe the irrotational dust component of the universe in terms of a relativistic gradient expansion and transform the resulting synchronous metric to a Newtonian coordinate system. The two metrics are connected via a space-like displacement field and a time-like perturbation, providing a relativistic generalization of the transformation from Lagrangian to Eulerian coordinates. The relativistic part of the displacement field generates already at initial time a non-local density perturbation at second order. This is a purely relativistic effect since it originates from space-time mixing. We give two options, the passive and the active approach, on how to include the relativistic corrections for example in N-body simulations. In the passive approach we treat the corrections as a non-Gaussian modification of the initial Gaussian field (primordial non-Gaussianity could be incorporated as well). The induced non-Gaussianity depends on scale and the redshift at which initial conditions are set, with f_NL ~ few for small enough scales and redshifts. In the active approach we show how to use the relativistic trajectory to obtain the initial displacement and velocity of particles for N-body simulations without modifying the initial Gaussian field.

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