Research in Gravitation Theory (Physics)

研究早期宇宙的三个主要问题：第一个是求解非共形耦合自由标量场在齐次和各向同性时空中存在时的半经典反反应方程。这其中有两个方面特别令人感兴趣。一个是解的初始行为，因为这将决定它们是否有初始奇点或粒子视界。二是Starobinsky的暴胀模型和Mijic等人的R模型如何受到暴胀阶段非共形场存在的影响。第二个研究项目是求解各向异性时空中自由标量场的反反应问题。观察量子效应是否会改变这些时空中奇点的性质是很有趣的。此外，还将获得通过粒子产生而在各种模型中耗散的各向异性数量的定量预测。第三个研究项目将是研究具有四次自耦合的N标量场模型在具有紧致空间截面的时空中自发对称性破缺。已经证明，这些模型在大N极限下的自发对称性破缺在爱因斯坦宇宙中不会发生。如果这个结果更普遍，那么它可能对宇宙学非常重要。

Research on three major problems concerned with the early universe will be conducted: The first consists of solving the semiclassical backreaction equations when nonconformally coupled free scalar fields are present in homogeneous and isotropic spacetimes. Two aspects of this are of particular interest. One is the initial behaviors of the solutions, as that will determine whether they have initial singularities or particle horizons. The second is how Starobinsky's inflationary models and the R models of Mijic et. al. are affected by the presence of non-conformal fields during the inflationary phase. The second research project consists of solving the backreaction problem for free scalar fields in anisotropic spacetimes. It is of interest to see whether quantum effects change the nature of the singularities in these spacetimes. Also quantitative predictions for the amounts of anisotropy that can be dissipated in various models via particle production will be obtained. The third research project will be an investigation of spontaneous symmetry breaking in spacetimes with compact spatial sections for models with N scalar fields with quartic self- couplings. It has already been shown that spontaneous symmetry breaking for these models in the large N limit does not occur in the Einstein universe. If this result is more general, then it may be of great importance to cosmology.