基于圈量子宇宙学有效理论框架下的暖暴涨在超暴涨阶段的性质研究

Loop quantum cosmology (LQC) inherits the framework developed from the loop quantum gravity. The aim of loop quantum cosmology is to quantize the homogeneous and isotropic cosmological model. Since the beginning of this century, LQC and the applications of the effective theory of LQC have been discussed by many authors and got a lot of meaningful results. This theory provides a good platform for understanding the very early Universe. Just as standard inflationary theory, warm inflation, which considers scalar field is interacting with radiation, is another model of inflationary theory. In this project, we will discuss the warm super-inflation in effective loop quantum cosmology. Considering the interaction between scalar field and radiation, we will investigate the relationship between the potential of scalar field and the e-folding number during super-inflation; study the connection between the dissipation coefficient and the e-folding number; analyze the evolution pictures of scalar field and radiation during super-inflation, and discuss the difference of results between warm inflation and standard inflation in this project.

圈量子宇宙学是采用圈量子引力的方案来量子化均匀和各向同性的宇宙学模型。自其本世纪初提出到现在，该理论及其有效理论被大量研究并取得了许多有意义的结论，为理解极早期宇宙提供了良好的平台。暖暴涨考虑暴涨场与辐射之间存在相互作用，与标准暴涨一样，是研究暴涨理论的一个重要分支。本申请项目中，拟对基于圈量子宇宙学的有效理论框架下的暖暴涨在超暴涨阶段的性质进行研究。本项目主要目的包括：考虑在超暴涨阶段标量场与辐射之间存在相互作用，研究标量场势能对超暴涨阶段的 e 叠数的影响； 探讨不同衰减因子对 e 叠数的影响；分析超暴涨阶段标量场、辐射的演化情况并讨论其与标准暴涨之间的差异。

本项目拟对圈量子宇宙学有效理论框架下的暖暴涨在超薄涨阶段的性质进行研究。在本项目资助下，项目负责人从现象学的角度讨论了圈量子宇宙学中的超薄涨性质。考虑宇宙充满相互作用的有质量标量场和辐射。考虑衰减系数为常数，并考虑四种不同初值条件，我们分析了超薄涨阶段的尺度因子的变化，我们发现超薄涨阶段的尺度因子的变化依赖于标量场和辐射在反弹点处的初值条件，但无论初值条件为哪种情况，宇宙最终都将进入辐射主导；同时，我们也发现，选择不同的衰减系数，超薄涨阶段的尺度因子变化会不同。另一方面，我们讨论了超薄涨阶段是否可以提供足够的e叠数。考虑到超薄涨开始于量子反弹点，此时Hubble参数H～0，从而超薄涨阶段有可能解决平直性和视界问题。