标题： 暴胀关联函数的算符乘积展开与德西特的共形对称性 显示英文标题

标题： Operator Product Expansion of Inflationary Correlators and Conformal Symmetry of de Sitter

摘要： 我们研究多场暴胀模型，其中宇宙扰动由除了暴胀场以外的轻标量场产生。 相应的扰动既具有尺度不变性又具有特殊共形不变性。 我们利用共形场论的算符乘积展开技术来研究在德西特时期存在对称性的暴胀关联函数。 算符乘积展开在表征两个观测上有兴趣的极限中的暴胀关联函数时特别强大，即三阶关联函数的挤压极限和四阶关联函数的坍缩极限。 尽管德西特对称性并未固定四阶关联函数的形状，但通过利用算符乘积展开可以在坍缩极限中找到其精确形状。 通过利用共形不变性使轻场的两阶交叉相关性消失，除非这些场具有相同的共形权重，我们能够证明Suyama-Yamaguchi不等式，该不等式将挤压极限中双谱的系数$f_{\rm NL}$与坍缩极限中四谱的系数$\tau_{\rm NL}$联系起来，在轻场本身具有非高斯性的情况下也成立。 事实上，我们证明该不等式无论是否存在共形对称性都成立，只是基本物理原理（如算符乘积的短距离展开）的结果。 因此，如果观察到该不等式的强烈违背，将对暴胀模型有深远的影响，因为它将意味着多场暴胀不能独立于模型细节产生观测到的涨落，或者在暴胀期间某些新的非平凡自由度起作用。 显示英文摘要

摘要： We study the multifield inflationary models where the cosmological perturbation is sourced by light scalar fields other than the inflaton. The corresponding perturbations are both scale invariant and special conformally invariant. We exploit the operator product expansion technique of conformal field theories to study the inflationary correlators enjoying the symmetries present during the de Sitter epoch. The operator product expansion is particularly powerful in characterizing inflationary correlation functions in two observationally interesting limits, the squeezed limit of the three-point correlator and the collapsed limit of the four-point correlator. Despite the fact that the shape of the four-point correlators is not fixed by the symmetries of de Sitter, its exact shape can be found in the collapsed limit making use of the operator product expansion. By employing the fact that conformal invariance imposes the two-point cross-correlations of the light fields to vanish unless the fields have the same conformal weights, we are able to show that the Suyama-Yamaguchi inequality relating the coefficients $f_{\rm NL}$ of the bispectrum in the squeezed limit and $\tau_{\rm NL}$ of the trispectrum in the collapsed limit also holds when the light fields are intrinsically non-Gaussian. In fact, we show that the inequality is valid irrespectively of the conformal symmetry, being just a consequence of fundamental physical principles, such as the short-distance expansion of operator products. The observation of a strong violation of the inequality will then have profound implications for inflationary models as it will imply either that multifield inflation cannot be responsible for generating the observed fluctuations independently of the details of the model or that some new non-trivial degrees of freedom play a role during inflation.