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arXiv 1504.05935astro-ph.COhep-th
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单场暴胀中是否存在尺度依赖的偏倚？

Is There Scale-Dependent Bias in Single-Field Inflation?

Roland de Putter, Olivier Doré, Daniel Green

备注：
25 pages; v2 matches version published in JCAP (only minor changes relative to v1)
发表信息：
JCAP, Issue 10, article id. 024, (2015)
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摘要：

由于局部原始非高斯性而产生的与尺度相关的晕轮偏差提供了对单场暴胀的强有力检验。虽然人们普遍认为，与当前观测的不确定性相比，单场暴胀预测的尺度依赖偏差可以忽略不计，但对于尺度依赖偏差的确切水平仍然存在分歧，这种水平可能会强烈影响未来调查的推断。在本文中，我们澄清了这一混乱，并从不同的角度推导出在单场暴胀中完全存在零尺度依赖偏差。目前的困惑主要来自于这样一个事实，即单场暴胀确实预测了$f_{NL}^{loc} \approx -5/3$水平上物质扰动的模式耦合，这会天真地导致尺度依赖性偏差。然而，我们明确地表明，这种模式耦合抵消时，在一个固定的物理尺度，而不是固定的坐标尺度的扰动进行评估。此外，我们还展示了如何在任何规范中容易地导出不存在标度依赖的偏差。然后，这一结果可以被纳入一个完整的描述所观察到的星系团，包括以前研究的广义相对论的条款，这是重要的，在同一水平的尺度依赖偏差的顺序$f_{NL}^{loc} \sim 1$。这种描述将使我们能够从未来的星系团数据中得出关于暴胀的无偏见的结论。

英文摘要：

Scale-dependent halo bias due to local primordial non-Gaussianity provides a strong test of single-field inflation. While it is universally understood that single-field inflation predicts negligible scale-dependent bias compared to current observational uncertainties, there is still disagreement on the exact level of scale-dependent bias at a level that could strongly impact inferences made from future surveys. In this paper, we clarify this confusion and derive in various ways that there is exactly zero scale-dependent bias in single-field inflation. Much of the current confusion follows from the fact that single-field inflation does predict a mode coupling of matter perturbations at the level of $f_{NL}^{loc} \approx -5/3$, which naively would lead to scale-dependent bias. However, we show explicitly that this mode coupling cancels out when perturbations are evaluated at a fixed physical scale rather than fixed coordinate scale. Furthermore, we show how the absence of scale-dependent bias can be derived easily in any gauge. This result can then be incorporated into a complete description of the observed galaxy clustering, including the previously studied general relativistic terms, which are important at the same level as scale-dependent bias of order $f_{NL}^{loc} \sim 1$. This description will allow us to draw unbiased conclusions about inflation from future galaxy clustering data.

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