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arXiv 1703.08809astro-ph.CO
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为什么没有牛顿反作用

Why there is no Newtonian backreaction

Nick Kaiser

备注：
6 pages, 0 figures. Substantially revised in response to reviewer's suggestions
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摘要：

在宇宙动力学的传统框架中，尺度因子$a(t)$被假定为服从一个完全均匀宇宙的“背景”弗里德曼方程，而粒子则根据密度涨落引力驱动的运动方程运动。最近有人提出，结构的出现通过牛顿（或“动力学”）逆反应改变了$a(t)$的演化，这可能避免了对暗能量的需要。本文指出，传统的方程组在牛顿引力中是精确的，而对于$a(t)$，使用齐次宇宙方程是没有近似性的。最近提出的修改Racz等人\（2017）在低速极限下并不还原为牛顿引力。我们讨论的关系，这对“广义弗里德曼方程”的布歇特和埃勒斯。这些是完全不同的东西;他们的公式描述了个别区域，并且是在物质表现得像无压流体的限制性假设下获得的，而我们的结果对于无碰撞动力学是精确的，并且是结构方程中出现的辅助关系。我们使用的一般速度自相关函数的对称性，以显示如何布歇特的$\cal Q$往往非常迅速地为零的大体积，这并不简单地出现"建设“通过采用周期性的边界条件，因为已经声称。我们的结论是，在牛顿引力准确描述低$z$宇宙的程度上，$a(t)$上没有结构的反作用，并且对暗能量的需要不能以这种方式避免。

英文摘要：

In the conventional framework for cosmological dynamics the scale factor $a(t)$ is assumed to obey the `background' Friedmann equation for a perfectly homogeneous universe while particles move according to equations of motions driven by the gravity of the density fluctuations. It has recently been suggested that the emergence of structure modifies the evolution of $a(t)$ via Newtonian (or `kinematic') backreaction and that this may avoid the need for dark energy. Here we point out that the conventional system of equations is exact in Newtonian gravity and there is no approximation in the use of the homogeneous universe equation for $a(t)$. The recently proposed modification of Racz et al.\ (2017) does not reduce to Newtonian gravity in the limit of low velocities. We discuss the relation of this to the `generalised Friedmann equation' of Buchert and Ehlers. These are quite different things; their formula describes individual regions and is obtained under the restrictive assumption that the matter behaves like a pressure-free fluid whereas our result is exact for collisionless dynamics and is an auxiliary relation appearing in the structure equations. We use the symmetry of the general velocity autocorrelation function to show how Buchert's $\cal Q$ tends very rapidly to zero for large volume and that this does not simply arise `by construction' through the adoption of periodic boundary conditions as has been claimed. We conclude that, to the extent that Newtonian gravity accurately describes the low-$z$ universe, there is no backreaction of structure on $a(t)$ and that the need for dark energy cannot be avoided in this way.

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