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arXiv 1507.02255astro-ph.CO
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关于暗物质密度场微扰方法的可达性

On the reach of perturbative methods for dark matter density fields

Tobias Baldauf, Emmanuel Schaan, Matias Zaldarriaga

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22 pages, 10 figures
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摘要：

本文在大尺度结构的有效场论（EFT）的背景下研究了从拉格朗日空间到欧拉空间的映射。我们用拉格朗日微扰理论（LPT）计算拉格朗日位移，并执行从位移到密度的完全非微扰变换。当扩展到给定的阶数时，这种变换再现了相同阶数的标准欧拉微扰理论（SPT）。然而，从位移到密度的完全变换还包括高阶项。这些术语明确地恢复长波长运动，从而使所得的密度场更好地与真正的非线性密度场相关。因此，该方法的有效性机制有望扩展欧拉EFT的有效性机制，并与IR-规范化的欧拉EFT的有效性机制相匹配。因此，这种方法有效地实现了在现场水平上对IR-图形化EFT的测试。我们估计的大小随机，非微扰贡献的物质密度功率谱。我们发现在我们的最高阶计算中，在红移z=0时，密度场的功率谱在k=0.25 h/Mpc（k=0.46 h/Mpc）时以1%（10%）的精度再现。我们认为，剩余误差的主要来源是随机贡献。不幸的是，在这些尺度上，随机项还没有像在非常低的k状态下那样缩放为$k^4$。因此，模拟这种贡献可能具有挑战性。

英文摘要：

We study the mapping from Lagrangian to Eulerian space in the context of the Effective Field Theory (EFT) of Large Scale Structure. We compute Lagrangian displacements with Lagrangian Perturbation Theory (LPT) and perform the full non-perturbative transformation from displacement to density. When expanded up to a given order, this transformation reproduces the standard Eulerian Perturbation Theory (SPT) at the same order. However, the full transformation from displacement to density also includes higher order terms. These terms explicitly resum long wavelength motions, thus making the resulting density field better correlated with the true non-linear density field. As a result, the regime of validity of this approach is expected to extend that of the Eulerian EFT, and match that of the IR-resummed Eulerian EFT. This approach thus effectively enables a test of the IR-resummed EFT at the field level. We estimate the size of stochastic, non-perturbative contributions to the matter density power spectrum. We find that in our highest order calculation, at redshift z=0 the power spectrum of the density field is reproduced with an accuracy of 1 % (10 %) up to k=0.25 h/Mpc (k=0.46 h/Mpc). We believe that the dominant source of the remaining error is the stochastic contribution. Unfortunately, on these scales the stochastic term does not yet scale as $k^4$ as it does in the very low-k regime. Thus, modeling this contribution might be challenging.

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