Non-gaussianity and scalar-induced gravitational waves from ghost inflation

    In this thesis, we calculate and analyze the non-Gaussianity and the power spectrum of scalar-induced gravitational waves in the theory of Ghost Inflation. Ghost inflation predicts almost scale-invariant primordial cosmological perturbations with relatively large non-Gaussianity. The study of non-Gaussianity and induced gravitational waves is of great significance to the evolution of the universe. The non-Gaussianity could provide valuable information to distinguish different inflationary models, and through the non-Gaussianity we can understand the inflation is driven by which field naturally. The scalar induced gravitational wave provides the information of the small scale of the universe, and can constrain the inflationary models.
    We consider the scalar sector as the source for the parity-violation. Due to the isotropy of our universe, the parity-violating information in the scalar sector can not be obtained in the 2-point and 3-point, and therefore 4-point correlation function is the lowest-order for the scalar sector parity-violation. In terms of parity symmetry, there are two types of 4-point functions, which is the parity-even and parity-odd 4-point correlation function. In ghost inflation we can get the parity-odd quartic operators. We calculate these two types of trispectrum under the in-in formalism. Due to the parity-odd quartic action contains odd number of derivative with respect to the spatial coordinate. So different with the parity-even trispetrum, the parity-odd trispectrum is a purely imaginary function. In this thesis, we specifically calculate these two types of trispectrum, and calculate the corresponding scalar-induced gravitational wave energy density in the theory of Ghost Inflation. For the trispectrum, we consider some different configurations of momentum. The first is the equilateral limit, where we analyze and plot the shape functions. We also consider the configurations of momenta in the case of some particular limit, including the squeezed limit where one of the four momenta is much smaller than others and the folded limit where two pairs of the four momenta have the same length and opposite directions. We also verify the consistency relations using these two configurations. For the scalar-induced gravitational wave, we numerically calculate both the power spectrum- and trispectrum-induced contributions. We specifically calculate and analyze the right- and left-hand polarizations of GW for the chiral polarizations. For the parity-even trispectrum-induced power spectra of gravitational waves, the left- and right-hand power spectrum is identical. However, the parity-odd trispectrum makes the power spectrum of right- and left-hand polarizations different. We also calculate the chirality parameter to quantify the degree of parity-violation.

    在本文中，我们计算并分析了Ghost暴涨模型中产生的非高斯性以及诱导引力波的功率谱。 Ghost 暴涨模型预测了尺度不变的原初扰动的功率谱和相对较大的非高斯性。 研究非高斯性和诱导引力波对探测早期宇宙的演化有着重要的意义。对非高斯型的研究有助于区分不同的暴涨模型，即通过对此的研究可以让我们了解到究竟是何种场驱动了宇宙的暴涨。对诱导引力波的研究可以为小尺度的宇宙演化提供信息, 并且能够为暴涨模型提供约束。我们考虑标量扰动部分作为宇宙中宇称破缺信号的来源。由于宇宙的各向同性和均匀性，宇宙破缺的信号不能在二点和三点关联函数之中，因此标量的四点关联函数是最低阶的宇称破缺的来源。按照宇称来说，我们考虑了两类四点关联函数，分别是具有偶宇称的四点关联函数和具有奇宇称的四点关联函数。在Ghost 暴涨模型中我们可以得到具有奇宇称的四阶相互作用量。 在 In-In 框架之下我们计算了这两类四点关联函数。由于具有奇宇称的四阶相互作用量中含有奇数个对空间坐标的导数，也就是说，如果我们翻转空间坐标，那么相对应的哈密顿量将会有一个负号的产生。 因此，不同于具有偶宇称的四点关联函数，具有奇宇称的四点关联函数是一个纯虚的函数。在文章中我们具体的计算了这两类四点关联函数和相应的诱导引力波的功率谱。之后我们计算了不同的动量配置，我们考虑了等边的四动量结构，并且绘制了四点关联函数在这些结构下的曲面图。 我们也考虑了两种不同的动量极限形式，一是挤压极限，即某一个动量的长度趋向于0，一是折叠极限，即四个动量中有两对长度相同但方向相反的动量。在这两种极限形式下，我们验证了四点关联函数和三点关联函数之间的一致性关系。 对于诱导引力波，我们具体的分析了在手性坐标系下的诱导引力波的功率谱，并计算了了四点关联函数和两点关联函数诱导的引力波的功率谱。对于偶宇称的四点关联函数诱导的引力波的功率谱来说，左旋和右旋的功率谱是相同的。然而，对于奇宇称的四点关联函数诱导的引力波的功率谱，其左旋引力波和右旋引力波的功率谱不是相同的，我们计算了两者之间的差值 。 并且按照此差值, 我们计算了chirality 参数来衡量宇称破缺的大小。

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