非最小自燃三谱
The Non-Minimal Ekpyrotic Trispectrum
摘要：
利用微扰论中的协变形式，导出了两个非正则场空间度规的标量场的三阶演化方程。这些方程可用于多场宇宙学模型的局部双谱和三谱的预测。我们的主要应用是通过非最小熵机制产生原始曲率扰动的ekpyrotic模型。在这些模型中，由于两个标量场之间的非最小动力学耦合，首先产生几乎尺度不变的熵扰动，随后这些扰动被转换为曲率扰动。值得注意的是，熵扰动消失的双和三光谱在ekpyrotic阶段。然而，正如我们所展示的，曲率扰动的转换过程会导致局部非高斯参数$f_{NL}$和$g_{NL}$在不久的将来观测应该可以检测到的水平。事实上，为了获得曲率扰动的足够大的幅度和足够小的双谱，如在电流测量中所见，转换过程必须非常有效。有趣的是，对于这种有效的转换，三谱参数$g_{NL}$仍然是负的，并且通常具有${\cal O}(10^2) - {\cal O}(10^3),$的幅度，从而导致非最小耦合ekpyrotic模型的显著特征。
英文摘要：
Employing the covariant formalism, we derive the evolution equations for two scalar fields with non-canonical field space metric up to third order in perturbation theory. These equations can be used to derive predictions for local bi- and trispectra of multi-field cosmological models. Our main application is to ekpyrotic models in which the primordial curvature perturbations are generated via the non-minimal entropic mechanism. In these models, nearly scale-invariant entropy perturbations are generated first due to a non-minimal kinetic coupling between two scalar fields, and subsequently these perturbations are converted into curvature perturbations. Remarkably, the entropy perturbations have vanishing bi- and trispectra during the ekpyrotic phase. However, as we show, the conversion process to curvature perturbations induces local non-Gaussianity parameters $f_{NL}$ and $g_{NL}$ at levels that should be detectable by near-future observations. In fact, in order to obtain a large enough amplitude and small enough bispectrum of the curvature perturbations, as seen in current measurements, the conversion process must be very efficient. Interestingly, for such efficient conversions the trispectrum parameter $g_{NL}$ remains negative and typically of a magnitude ${\cal O}(10^2) - {\cal O}(10^3),$ resulting in a distinguishing feature of non-minimally coupled ekpyrotic models.
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