含张量的三点函数的一致性关系检验
Examining the consistency relations describing the three-point functions involving tensors
摘要：
众所周知，表征标量双谱的非高斯参数$f_{_{\rm NL}}$可以用压缩极限下的标量谱指数来表示，这一性质被称为相容关系。本文研究了由单个正则标量场驱动的暴胀模型中标量和张量的三点互相关以及张量双谱的相容关系。用我们前面介绍过的无量纲非高斯参数$C_{_{\rm NL}}^{\mathcal R}$和$C_{_{\rm NL}}^{\mathcal γ}$来表征互相关，我们以类似于纯标量情况的方式，将控制互相关的一致性关系表示为这些非高斯参数与标量或张量谱指数之间的关系。讨论了描述张量双谱的非高斯参数$h_{_{\rm NL}}$的对应关系。我们分析建立这些一致性关系明确在以下两种情况下：一个简单的例子，涉及一个特定的情况下，幂律膨胀和一个非平凡的情况下，在所谓的Starobinsky模型，是由一个线性的潜力，其斜率急剧变化。我们还在数值上验证了三种类型的通货膨胀模型，允许从慢卷的偏差，并导致标量功率谱的功能，通常会导致一个更好的适合的数据比更传统的，几乎规模不变的，光谱的一致性关系。最后，我们总结了我们所取得的成果。（节录）
英文摘要：
It is well known that the non-Gaussianity parameter $f_{_{\rm NL}}$ characterizing the scalar bi-spectrum can be expressed in terms of the scalar spectral index in the squeezed limit, a property that is referred to as the consistency relation. In this work, we consider the consistency relations associated with the three-point cross-correlations involving scalars and tensors as well as the tensor bi-spectrum in inflationary models driven by a single, canonical, scalar field. Characterizing the cross-correlations in terms of the dimensionless non-Gaussianity parameters $C_{_{\rm NL}}^{\mathcal R}$ and $C_{_{\rm NL}}^{\mathcal γ}$ that we had introduced earlier, we express the consistency relations governing the cross-correlations as relations between these non-Gaussianity parameters and the scalar or tensor spectral indices, in a fashion similar to that of the purely scalar case. We also discuss the corresponding relation for the non-Gaussianity parameter $h_{_{\rm NL}}$ used to describe the tensor bi-spectrum. We analytically establish these consistency relations explicitly in the following two situations: a simple example involving a specific case of power law inflation and a non-trivial scenario in the so-called Starobinsky model that is governed by a linear potential with a sharp change in its slope. We also numerically verify the consistency relations in three types of inflationary models that permit deviations from slow roll and lead to scalar power spectra with features which typically result in an improved fit to the data than the more conventional, nearly scale invariant, spectra. We close with a summary of the results we have obtained. (Abridged)
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