标题： 宇宙膨胀模型中的非高斯性和统计各向异性 显示英文标题

标题： Non-gaussianity and Statistical Anisotropy in Cosmological Inflationary Models

摘要： 我们研究了一些宇宙膨胀模型的统计描述符，这些模型允许产生高水平的非高斯性和统计各向异性破缺。基本上，我们研究了两类不同的模型：一类只包含标量场扰动，具体来说是一类小场慢滚膨胀模型的子类，其动能项具有规范形式；另一类则允许同时存在矢量场和标量场扰动。我们研究前者是为了表明可以在双谱 B_\zeta 和三谱 T_\zeta 的非高斯性参数 f_{非线性}、\tao _{非线性} 中达到非常高的（包括可观测的）值，分别对应原初曲率扰动 \zeta 。 通过考虑谱 \( P_\{\text\{\zeta \}\} \)、双谱 \( B_\{\text\{\zeta \}\} \) 和三谱 \( T_\{\text\{\zeta \}\} \) 中的环路修正，得到了这样一个结果。即使\zeta 在暴胀期间产生，\( f_\{\text\{{非线性}\}\} \) 和 \( \text\{\tao \}_\{\text\{{非线性}\}\} \) 也会出现可观测的值。 For the latter we study the spectrum P_\zeta , bispectrum B_\zeta and trispectrum \$T_\zeta of the primordial curvature perturbation when \zeta is generated by scalar and vector field perturbations. The tree-level and one-loop contributions from vector field perturbations are worked out considering the possibility that the one-loop contributions may be dominant over the tree level terms. 计算了非高斯性水平 f_{非线性} 和 \tao _{非线性}，并将它们与功率谱中的统计各向异性水平 g_\zeta 相关联。 对于功率谱中非常小的统计各向异性，非高斯性水平可能非常高，在某些情况下甚至超过了当前的观测限制。 显示英文摘要

摘要： We study the statistical descriptors for some cosmological inflationary models that allow us to get large levels of non-gaussianity and violations of statistical isotropy. Basically, we study two different class of models: a model that include only scalar field perturbations, specifically a subclass of small-field slow-roll models of inflation with canonical kinetic terms, and models that admit both vector and scalar field perturbations. We study the former to show that it is possible to attain very high, including observable, values for the levels of non-gaussianity f_{NL} and \tao_{NL} in the bispectrum B_\zeta and trispectrum T_\zeta of the primordial curvature perturbation \zeta respectively. Such a result is obtained by taking care of loop corrections in the spectrum P_\zeta, the bispectrum B_\zeta and the trispectrum T_\zeta . Sizeable values for f_{NL} and \tao_{NL} arise even if \zeta is generated during inflation. For the latter we study the spectrum P_\zeta, bispectrum B_\zeta and trispectrum $T_\zeta of the primordial curvature perturbation when \zeta is generated by scalar and vector field perturbations. The tree-level and one-loop contributions from vector field perturbations are worked out considering the possibility that the one-loop contributions may be dominant over the tree level terms. The levels of non-gaussianity f_{NL} and \tao_{NL}, are calculated and related to the level of statistical anisotropy in the power spectrum, g_\zeta . For very small amounts of statistical anisotropy in the power spectrum, the levels of non-gaussianity may be very high, in some cases exceeding the current observational limit.