标题： 模不变 inflation、再加热和轻子生成 显示英文标题

标题： Modular invariant inflation, reheating and leptogenesis

摘要： 我们利用模对称性作为组织原则，试图同时解决轻子味问题、暴胀、暴胀后再加热以及宇宙学生成问题。 我们在轻子部门通过有限的模群 $A_4$ 展示了这种方法。 在我们的模型中，中微子质量是通过 I 型见反机制生成的，模对称性决定了 Yuka 耦合和右手中微子质量的形式。 模场还驱动暴胀，与最近的宇宙微波背景 (CMB) 观测值非常吻合。 张量到标量比的相应预测非常小，为 $r \sim \mathcal{O}(10^{-7})$，而谱指数运行的预测 $\alpha \sim -\mathcal{O}(10^{-3})$ 可能在不久的将来得到检验。 该设置的一个吸引人之处在于，为了再加热所需的暴胀物质相互作用自然地来自相关模形式的展开。 尽管相应的暴胀衰变率受到普朗克尺度的抑制，但再加热温度仍然可以足够高以确保成功的大爆炸核合成。 我们发现，负责再加热的相同耦合也通过非热轻子生成贡献了部分宇宙的重子不对称性。 显示英文摘要

摘要： We use modular symmetry as an organizing principle that attempts to simultaneously address the lepton flavor problem, inflation, post-inflationary reheating, and baryogenesis. We demonstrate this approach using the finite modular group $A_4$ in the lepton sector. In our model, neutrino masses are generated via the Type-I see-saw mechanism, with modular symmetry dictating the form of the Yukawa couplings and right-handed neutrino masses. The modular field also drives inflation, providing an excellent fit to recent Cosmic Microwave Background (CMB) observations. The corresponding prediction for the tensor-to-scalar ratio is very small, $r \sim \mathcal{O}(10^{-7})$, while the prediction for the running of the spectral index, $\alpha \sim -\mathcal{O}(10^{-3})$, could be tested in the near future. An appealing feature of the setup is that the inflaton-matter interactions required for reheating naturally arise from the expansion of relevant modular forms. Although the corresponding inflaton decay rates are suppressed by the Planck scale, the reheating temperature can still be high enough to ensure successful Big Bang nucleosynthesis. We find that the same couplings responsible for reheating also contribute to generating part of the baryon asymmetry of the Universe through non-thermal leptogenesis.