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arXiv 1009.0597astro-ph.CO
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微扰理论与晕模型的结合

Combining perturbation theories with halo models

Patrick Valageas, Takahiro Nishimichi

摘要:

我们调查的统一模型的建设,可以预测的物质密度功率谱和两点关联函数从很大到很小的尺度,是一致的微扰理论在低$k$和晕模型在高$k$。我们使用拉格朗日框架来重新解释晕模型,并将功率谱分解为“2-晕”和“1-晕”的贡献,涉及到“微扰”和“非微扰”的条款。我们描述了一个简单的实现这个模型,并提出了详细的比较与数值模拟,从$k \sim 0.02$到$100 h$ Mpc $^{-1}$,从$x \sim 0.02$到$150 h^{-1}$ Mpc。我们发现,1-halo贡献包含一个计数项,确保$k^2$尾巴在低$k$和重要的是不破坏预测的尺度探测重子声学振荡,$k \sim 0.02$ $0.3 h$ Mpc $^{-1}$。另一方面,我们表明,标准的微扰理论是不够的2-halo的贡献,因为高阶项增长太快,在高$k$,因此,必须使用remmation计划。我们描述了一个简单的实现,基于1-循环“直接最陡下降”remmation的2晕的贡献,允许快速数值计算,我们检查,我们得到了很好的匹配,以模拟在低和高$k$。我们简单的实现已经票价优于标准的1-回路扰动理论在大尺度上和简单的适合在高$k$的功率谱,具有典型的精度为1%的大尺度和10%的小尺度。对于两点关联函数,我们也得到了类似的结果。然而,仍然有改进的空间之间的2-halo和1-halo的贡献,这可能是最困难的制度来描述的过渡尺度。

英文摘要:

We investigate the building of unified models that can predict the matter-density power spectrum and the two-point correlation function from very large to small scales, being consistent with perturbation theory at low $k$ and with halo models at high $k$. We use a Lagrangian framework to re-interpret the halo model and to decompose the power spectrum into "2-halo" and "1-halo" contributions, related to "perturbative" and "non-perturbative" terms. We describe a simple implementation of this model and present a detailed comparison with numerical simulations, from $k \sim 0.02$ up to $100 h$Mpc$^{-1}$, and from $x \sim 0.02$ up to $150 h^{-1}$Mpc. We show that the 1-halo contribution contains a counterterm that ensures a $k^2$ tail at low $k$ and is important not to spoil the predictions on the scales probed by baryon acoustic oscillations, $k \sim 0.02$ to $0.3 h$Mpc$^{-1}$. On the other hand, we show that standard perturbation theory is inadequate for the 2-halo contribution, because higher order terms grow too fast at high $k$, so that resummation schemes must be used. We describe a simple implementation, based on a 1-loop "direct steepest-descent" resummation for the 2-halo contribution that allows fast numerical computations, and we check that we obtain a good match to simulations at low and high $k$. Our simple implementation already fares better than standard 1-loop perturbation theory on large scales and simple fits to the power spectrum at high $k$, with a typical accuracy of 1% on large scales and 10% on small scales. We obtain similar results for the two-point correlation function. However, there remains room for improvement on the transition scale between the 2-halo and 1-halo contributions, which may be the most difficult regime to describe.

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