宇宙极早期暖暴涨理论的扩展及其微扰论研究

Warm inflation, as a candidate of inflationary theory in the very early universe, inherits most advantages of cold inflation - perfectly solves the horizon, flatness and monopole problems. Compared to cold inflation, the flatness requirement of inflaton potential in warm inflation is not so strict and the universe can go into the radiation dominated epoch smoothly without a separate reheating phase. In addition, warm inflation cures ``eta-problem" and overlarge amplitude of inflaton suffered in cold inflation. The density fluctuations in warm inflationary universe mainly originate from thermal fluctuations. Till now, most works in warm inflation still concentrate on single canonical scalar fields. Here, we aim to extend warm inflationary theory and calculate the stability and observable quantities of perturbation theory in extended theory. First, we extend warm inflation to noncanonical field whose Lagrangian density has separable form of kinetic term and potential term and multi-fields, calculate the slow roll conditions, temperature, e-folds, power spectrum，spectral index and non-Gaussianity etc in the extended new theory, and research the influence of thermal effect. In addition, we extend warm inflation to non-minimally derivative coupling theory, perform an entire stability analysis, and construct the perturbation theory in the extended theory. Finally, basing on the observation results, we reconstruct the general warm inflationary action. The reconstruction can be divided into kinetic term reconstruction and potential reconstruction respectively.

暖暴涨作为宇宙极早期暴涨理论的候选者之一，很好地解决了视界疑难，平直性疑难和磁单极子问题。相比于冷暴涨，暖暴涨对势能平坦性的要求不那么苛刻，不需重加热阶段就可光滑过渡到辐射主导时期，很好地解决了冷暴涨中的“eta-problem”和场振幅过大的问题。在暖暴涨中，宇宙密度涨落主要起源于热涨落。到目前为止，暖暴涨领域内的工作几乎都是针对单一正则场开展的。本项目中，我们将致力于扩展暖暴涨理论并计算扩展之后理论中的稳定性和微扰可观测量。首先，将暖暴涨扩展到动能势能耦合的非正则场和复合场中，计算新理论中的慢滚条件、温度、e叠数、功率谱、谱指数、非高斯性等物理量，研究热效应的影响。然后，把暖暴涨推广到non-minimally derivative coupling理论中，给出完整的稳定性分析，建立起推广后的微扰理论。最后，直接利用观测结果，分动能势能两部分重构出一般形式的暖暴涨作用量。

暖暴涨作为宇宙极早期暴涨理论的候选方案，很好地解决了视界疑难，平直性疑难和磁单极子问题。暖暴涨理论有它的复杂性，但也有很多优点，如势能平坦性的要求不那么苛刻，不需重加热阶段就可光滑过渡到辐射主导时期，很好地解决了冷暴涨中的“η-problem”和场振幅过大的问题。在暖暴涨中，宇宙密度涨落主要起源于热涨落。但这种值得深入研究的暴涨理论长期以来基本局限于单一正则场模型中。针对这一研究现状，本项目将暖暴涨理论做了很好的推广：①把暖暴涨推广到了一般的动能势能存在耦合的非正则场之中；②把暖暴涨理论推广到了以双场为代表的复合场之中；③系统地计算了推广后的暖暴涨理论的微扰可观测量，尤其是非高斯性问题；④把暖暴涨理论推广到了只含动能项的非正则场之中。