We consider a model of inflation consisting a triplet of $U(1)$ vector fields with the parity violating interaction which is non-minimally coupled to inflaton. The vector field sector enjoys global $O(3)$ symmetry which admits isotropic configuration and provides not only vector modes but also scalar and tensor modes. We decompose the scalar perturbations into the adiabatic, entropy and isocurvature perturbations and compute all power spectra and cross correlations of the scalar and the tensor sectors. The tensor modes associated with the vector fields contribute to the power spectrum of gravitational waves while the parity violating term generates chirality in gravitational power spectra and bispectra. We study nonlinear scalar and tensor perturbations and compute all bispectra and three-point cross-correlations. In particular, it is shown that the non-Gaussianity of curvature perturbations and gravitational waves are enhanced by the vector field perturbations. We show that non-Gaussianities put strong constraints on the model parameters such as the parity violating coupling and the fractional energy of the vector fields.

中文翻译：

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具有多个矢量场和非高斯性的通货膨胀

我们考虑一个暴胀模型，该模型由三个 $U(1)$ 向量场组成，其中具有与暴胀子非最小耦合的奇偶违反相互作用。矢量场扇区享有全局 $O(3)$ 对称性，允许各向同性配置，不仅提供矢量模式，还提供标量和张量模式。我们将标量扰动分解为绝热、熵和等曲率扰动，并计算标量和张量扇区的所有功率谱和互相关。与矢量场相关的张量模式对引力波的功率谱有贡献，而违反奇偶性的项在引力功率谱和双谱中产生手性。我们研究非线性标量和张量扰动并计算所有双谱和三点互相关。特别是，结果表明，矢量场扰动增强了曲率扰动和引力波的非高斯性。我们表明，非高斯性对模型参数（例如奇偶违反耦合和矢量场的分数能量）施加了强约束。