论文标题
公制植入几何形状的保形通胀
Conformal inflation in the metric-affine geometry
论文作者
论文摘要
从局部保形对称性的角度研究了对通货膨胀模型类别的系统理解，在公制植入几何形状的框架中，全局对称性略有破裂。在公制的植入几何形状中，这是对普通一般相对性中采用的riemannian的概括，仿射连接是度量的独立变量，而不是给定的，例如由Levi-Civita连接作为其函数。得益于这种独立性，公制的植入几何形状可以在拉格朗日的每个术语中保留局部的形式对称性，与里曼尼亚的几何形状相反，然后局部的保形不变性可以与更多类型的全球对称性兼容。作为简单的示例，我们考虑了带有损坏的$ \ mathrm {so}（1,1）$或$ \ mathrm {o}（2）$的两尺度模型，分别导致了众所周知的$α$ attractor或自然通货膨胀。充气可以理解为他们的伪Nambu-Goldstone玻色子。
Systematic understanding for classes of inflationary models is investigated from the viewpoint of the local conformal symmetry and the slightly broken global symmetry in the framework of the metric-affine geometry. In the metric-affine geometry, which is a generalisation of the Riemannian one adopted in the ordinary General Relativity, the affine connection is an independent variable of the metric rather than given e.g. by the Levi-Civita connection as its function. Thanks to this independency, the metric-affine geometry can preserve the local conformal symmetry in each term of the Lagrangian contrary to the Riemannian geometry, and then the local conformal invariance can be compatible with much more kinds of global symmetries. As simple examples, we consider the two-scalar models with the broken $\mathrm{SO}(1,1)$ or $\mathrm{O}(2)$, leading to the well-known $α$-attractor or natural inflation, respectively. The inflaton can be understood as their pseudo Nambu-Goldstone boson.
