A new approach to gravitational clustering: A path-integral formalism and large-N expansions
A new approach to gravitational clustering: A path-integral formalism and large-N expansions
复制标题
引力聚类的新方法：路径积分形式主义和大 N 展开
DOI：
10.1051/0004-6361:20040125
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发表时间：
2003
影响因子：
6.5
通讯作者：
P. Valageas
中科院分区：
文献类型：
--
作者：
P. Valageas
我们证明了在膨胀的宇宙中通过引力不稳定性形成的大尺度结构可以通过路径积分形式充分描述。我们推导了作用$S[f]$，它给出了与任何相空间分布函数$f({\vec x},{\vec p},t)$相关联的统计权值。这个作用S描述了高斯初始条件下的平均值和Vlasov-Poisson动力学。接下来，应用从场论中借鉴的标准方法，我们将问题推广到N场系统，并寻找$1/N$的幂展开式。我们描述了三种这样的方法，并推导了引力聚类在最低非平凡阶的相应运动方程。这为相空间分布f的均值$\overline{f}$和两点相关G以及响应函数R产生了一组非线性方程。这些系统方案与通常的准线性尺度上的微扰展开相匹配，但也应该能够处理非线性状态。我们的方法也可以扩展到非高斯初始条件，并可以作为从场论借鉴的其他工具的基础。
We show that the formation of large-scale structures through gravitational instability in the expanding universe can be fully described through a path-integral formalism. We derive the action $S[f]$ which gives the statistical weight associated with any phase-space distribution function $f({\vec x},{\vec p},t)$. This action S describes both the average over the Gaussian initial conditions and the Vlasov-Poisson dynamics. Next, applying a standard method borrowed from field theory we generalize our problem to an N -field system and we look for an expansion over powers of $1/N$. We describe three such methods and we derive the corresponding equations of motion at the lowest non-trivial order for the case of gravitational clustering. This yields a set of non-linear equations for the mean $\overline{f}$ and the two-point correlation G of the phase-space distribution f , as well as for the response function R . These systematic schemes match the usual perturbative expansion on quasi-linear scales but should also be able to treat the non-linear regime. Our approach can also be extended to non-Gaussian initial conditions and may serve as a basis for other tools borrowed from field theory.