AI 中文总结
本研究提出一种基于赝超势哈勃函数的解析方法，构建超越慢滚近似的可积暴胀模型，通过数值与半解析手段计算微扰谱并与观测及慢滚结果对比。
AI 中文摘要
我们提出了一种用于研究多组分FLRW宇宙学及其微扰的新型解析方法。该动力学由单个标量场触发，其标量势编码了多组分流体的能量密度和压强。这一描述将标准大爆炸宇宙学、暴胀模型和暗能量统一在同一个框架下。可积性的关键在于将标量势用充当赝超势的哈勃函数$H(ϕ)$来表示，从而将动力学转化为一阶问题，可在合适的时间坐标下解析求解。在此框架内，我们提出了若干可积暴胀模型，它们与文献中分析的模型具有相似性质且符合观测结果。最后，我们通过数值和（半）解析技术积分Mukhanov-Sasaki方程，研究了每个模型中的标量和张量宇宙学微扰。这使我们能够计算慢滚近似之外的功率谱、谱指数和张标比，并将我们的通用结果与当前可用的观测结果以及基于慢滚近似的理论预测进行对比。
英文摘要
We propose a novel analytic approach to the study of multi-component FLRW cosmologies and their perturbations. The dynamics is triggered by a single scalar field with a scalar potential codifying the energy density and pressure of the multi-component fluid. This description unifies standard Big Bang cosmologies, models of inflation and dark energy under a unique framework. The key to integrability is to express the scalar potential in terms of the Hubble function $H(ϕ)$ that plays the role of a fake superpotential, turning the dynamics into a first order problem, that may be analytically solved in a suitable time coordinate. In this framework, we propose integrable inflationary models with similar properties to the ones analysed in the literature and compatible with observations. Finally, we study scalar and tensor cosmological perturbations in each model by integrating Mukhanov-Sasaki equations via numerical and (semi-)analytic techniques. This allow us to compute the power spectrum, the spectral indices and the tensor-to-scalar ratio beyond the slow-roll approximation and compare our general results {against} the currently available observations and the theoretical predictions based on the slow-roll approximation.
Comments29 pages, 8 figures
