标题： 用CMB标量、矢量和张量三阶统计量探测早期宇宙 显示英文标题

标题： Probing the Early Universe with the CMB Scalar, Vector and Tensor Bispectrum

摘要： 尽管宇宙学观测表明种子场的涨落几乎是高斯的，但其场偏离高斯性的可能性被广泛讨论。理论上，存在许多暴胀场景，它们在原初扰动中预测了大而特征性的非高斯性。这些模型依赖的非高斯性是宇宙微波背景（CMB）三阶谱的来源；因此，分析CMB三阶谱对于阐明早期宇宙的本质非常重要且有吸引力。目前，已经对标量扰动中保留旋转和宇称不变性的原初非高斯性对CMB三阶谱的影响进行了深入研究。然而，尽管这一信息的重要性，对于涉及矢量和张量模式扰动并包含旋转或宇称不变性破坏的非高斯性产生的CMB三阶谱的复杂处理从未被考虑过。基于我们当前的研究，本论文提供了不仅针对标量模式扰动，而且针对矢量和张量模式扰动的CMB三阶谱的一般形式。应用这种形式，我们计算了由两个标量和一个引力子相关性产生的CMB三阶谱以及由原初磁场产生的CMB三阶谱，并概述了对这些振幅的新限制。此外，这种形式可以很容易地扩展到旋转或宇称不变性被破坏的情况。我们还计算了具有优选方向的曲率扰动的非高斯性以及由宇称破坏的Weyl三次项引起的引力子非高斯性的CMB三阶谱。我们还提出了一些这些对称性破坏对CMB三阶谱的独特影响。 显示英文摘要

摘要： Although cosmological observations suggest that the fluctuations of seed fields are almost Gaussian, the possibility of a small deviation of their fields from Gaussianity is widely discussed. Theoretically, there exist numerous inflationary scenarios which predict large and characteristic non-Gaussianities in the primordial perturbations. These model-dependent non-Gaussianities act as sources of the Cosmic Microwave Background (CMB) bispectrum; therefore, the analysis of the CMB bispectrum is very important and attractive in order to clarify the nature of the early Universe. Currently, the impacts of the primordial non-Gaussianities in the scalar perturbations, where the rotational and parity invariances are kept, on the CMB bispectrum have been well-studied. However, for a complex treatment, the CMB bispectra generated from the non-Gaussianities, which originate from the vector- and tensor-mode perturbations and include the violation of the rotational or parity invariance, have never been considered in spite of the importance of this information. On the basis of our current studies, this thesis provides the general formalism for the CMB bispectrum sourced by the non-Gaussianities not only in the scalar-mode perturbations but also in the vector- and tensor-mode perturbations. Applying this formalism, we calculate the CMB bispectrum from two scalars and a graviton correlation and that from primordial magnetic fields, and we then outline new constraints on these amplitudes. Furthermore, this formalism can be easily extended to the cases where the rotational or parity invariance is broken. We also compute the CMB bispectra from the non-Gaussianities of the curvature perturbations with a preferred direction and the graviton non-Gaussianities induced by the parity-violating Weyl cubic terms. We also present some unique impacts to the violation of these invariances on the CMB bispectrum.