论文标题
Jordan和Einstein框架的广义$ r^p $ - 吸引人的宇宙学：新型吸引子和重新审视标准的Jordan框架$ r^p $通货膨胀
Generalized $R^p$-attractor Cosmology in the Jordan and Einstein Frames: New Type of Attractors and Revisiting Standard Jordan Frame $R^p$ Inflation
论文作者
论文摘要
在这项工作中，我们将研究一种新的吸引子模型，我们将其称为广义$ r^p $ Attractor模型。这类模型基于$ r^p $ $ f（r）$重力模型的爱因斯坦框架电位的概括。我们介绍了相应的非最少耦合的约旦框架理论的吸引力特性，并计算了爱因斯坦框架中通货膨胀的观察指标。如我们所示，有大量的非最小耦合标量理论，具有任意的非最低耦合，满足某些条件，产生相同的爱因斯坦框架电位，这就是为什么这些模型被表征的吸引子的原因。正如我们所证明的那样，广义的$ r^p $ ATTRACTOR模型是可行的，并且在Planck约束中非常合适。这包括广义的$ r^p $ - 吸引者模型的子类，即约旦框架中$ r^p $通货膨胀的爱因斯坦框架电位，这是文献中也知道的。我们还重点介绍了与约旦框架中$ r^p $通货膨胀有关的重要问题，该框架是不可行的。通过保形的不变性，$ r^p $通货膨胀模型也应在约旦框架中可行，这不是。我们使用$ f（r）$ gravity jordan框架中的两种不同方法来指出问题的根源，正如我们所证明的，由于某些标准简化而出于分析性，文献中出现了问题。我们仅使用缓慢的滚动条件来展示正确分析约旦框架中$ r^p $通货膨胀的方法。
In this work we shall study a new class of attractor models which we shall call generalized $R^p$-attractor models. This class of models is based on a generalization of the Einstein frame potential of $R^p$ $f(R)$ gravity models in the Jordan frame. We present the attractor properties of the corresponding non-minimally coupled Jordan frame theory, and we calculate the observational indices of inflation in the Einstein frame. As we show, there is a large class of non-minimally coupled scalar theories, with an arbitrary non-minimal coupling which satisfies certain conditions, that yield the same Einstein frame potential, this is why these models are characterized attractors. As we demonstrate, the generalized $R^p$-attractor models are viable and well fitted within the Planck constraints. This includes the subclass of the generalized $R^p$-attractor models, namely the Einstein frame potential of $R^p$ inflation in the Jordan frame, a feature also known in the literature. We also highlight an important issue related to the $R^p$ inflation in the Jordan frame, which is known to be non-viable. By conformal invariance, the $R^p$ inflation model should also be viable in the Jordan frame, which is not. We pinpoint the source of the problem using two different approaches in the $f(R)$ gravity Jordan frame, and as we demonstrate, the problem arises in the literature due to some standard simplifications made for the sake of analyticity. We demonstrate the correct way to analyze $R^p$ inflation in the Jordan frame, using solely the slow-roll conditions.
