论文标题
palatini公式中二次重力的通货膨胀现象学
Inflationary phenomenology of quadratic gravity in the Palatini formulation
论文作者
论文摘要
一般相对论的理论是在配备度量张量的时空歧管上建立的，$（\ Mathcal {M} _4，\ text {g}）$，以及$ \ Mathcal {M {M} _4 $上的连接。即使有正当理由假设保留该度量的无扭转歧管，但表明处理这些假设，Levi-civita条件可以在GR的运动方程级别复制。不久之后，两种描述之间的一般相对性（称为palatini或一阶形式主义）之间的相等性，其中连接独立于指标，并且常规的度量或二阶形式主义被打破，以实现涉及更复杂的动作，涉及涉及高阶曲率不变的和/或非限定耦合的更为复杂的动作。如今，这些类型的理论在建模通货膨胀方面很重要，在他们发现了巨大的成功。由于通货膨胀的范式与重力自由度融合，因此其参数化融合在一起，因此有趣的是了解这些模型的预测如何在两种公式之间有所不同。出色的通货膨胀模型之一是Starobinsky或二次重力模型。但是，在Palatini形式主义中，由$ r^2 $术语提出的标量自由度是非动力的，无法推动通货膨胀阶段。为了使通货膨胀在一阶形式主义中实现，Starobinsky模型必须与基本的标量领域相结合，该模型将扮演充气的作用。在本文中，我们研究了以前排除在外模型开始的不同通货膨胀方案，我们发现$ r^2 $项在使爱因斯坦 - 框架的通电量平坦，从而为这些模型提供了与观察结果接触的机会。
The theory of General Relativity was established on a spacetime manifold equipped with a metric tensor, $(\mathcal{M}_4,\text{g})$, and the connection on $\mathcal{M}_4$ identified with the Levi-Civita one. Even though there are valid reasons to assume a torsionless manifold that preserves the metric, it was shown that dealing away with these assumptions the Levi-Civita condition can be reproduced at the level of equations of motion of GR. It was not long before the equivalence of General Relativity between the two descriptions, known as the Palatini or first-order formalism in which the connection is independent of the metric, and the conventional metric or second-order formalism, was broken for more complicated actions involving higher-order curvature invariants and/or nonminimal couplings between the gravitational and matter sector. Nowadays these types of theories are prominent in modeling inflation where they have found major success. Since the paradigm of inflation is fused with the gravitational degrees of freedom and thus their parametrisation, it is interesting to understand how the predictions of these models differ between the two formulations. One of the outstanding models of inflation is the Starobinsky or quadratic gravity model. However in the Palatini formalism the scalar degree of freedom sourced by the $R^2$ term is nondynamical and is unable to drive an inflationary phase. In order for inflation to be realised in the first-order formalism the Starobinsky model has to be coupled with a fundamental scalar field that will assume the role of the inflaton. In this thesis we investigate different inflationary scenarios, starting with previously ruled-out models, where we find that the $R^2$ term has a significant role in flattening the Einstein-frame inflaton potential and thus giving the opportunity for these models to come in contact with observations.
