Dynamical Symmetry Breaking in Curved Space-time

在宇宙膨胀的早期阶段，特别是在大统一理论时期，当暴胀发生时，宇宙受到保持时空弯曲的强经典引力的影响。暴胀膨胀是由希格斯场引起的。在普通的暴胀情景中，希格斯场被预先假定为“基本的”，它的真空期望值是一个自由参数。我们考虑了希格斯场是由一对费米子组成的复合场的可能性，并研究了这一假设的宇宙学后果。我们的研究结果总结如下：(1)采用Nambu-Jona-Lasinio模型作为复合希格斯模型的原型模型，研究了该模型在时空弯曲、温度和密度较高的早期宇宙条件下的相结构。我们发现了二阶相变。(2)采用实时形式的Schwinger-Dyson方程研究了有限温度下Abelian规范理论的相结构。我们发现了二阶相变的清晰信号。(3)在有限温度和曲率条件下，用1/N展开法研究了具有软超对称破缺项的超对称Nambu-Jona-Lasinio模型。我们发现一阶和二阶相变的发生取决于耦合常数和软断裂常数的强度。将上述结果应用于暴胀时代的宇宙，我们发现宇宙弦可能在这个时代产生。

At the early stage of the expanding universe, in particular at the period of grand unified theories when the inflation takes place, the universe is influenced by the strong classical gravity which keeps the space-time curved. The inflationary expansion is caused by the Higgs field. In the ordinary inflation scenario the Higgs field is preassumed to be 'elementary' and its vacuum expectation value is a free parameter. We considered the possibility that the Higgs field is a composite field composed of a pair of fermions and investigated the cosmological consequences of this assumption. Our results are summarized as follows;(1)As a prototype model of the composite Higgs model we adopt the Nambu-Jona-Lasinio model and studied the phase structure of the model under the condition of the early universe with curved space-time and high temperature and density. We found the 2nd order phase transition.(2)We studied the phase structure of Abelian gauge theories at finite temperature by using the Schwinger-Dyson equation in the real time formalism. We found the clear signal of the 2nd order phase transition.(3)We examined the supersymmetric Nambu-Jona-Lasinio model with a soft supersymmetry breaking term in the 1/N expansion method at finite temperature and curvature. We find that the 1st and 2nd order phase transition may take place depending on the strength of the coupling constant and the soft breaking constant.The above results were applied to the universe in the inflationary era and we find that the cosmic strings may be produced in this era.