论文标题
$ f（r）$ gravity的光谱指数和通货膨胀动态运行
Running of the Spectral Index and Inflationary Dynamics of $F(R)$ Gravity
论文作者
论文摘要
在这项工作中，我们将对真空$ f（r）$重力的频谱指数运行的模型一般计算。我们应利用光谱指数的功能形式和张量表与尺度比率的功能形式，以提出真空$ f（r）$重力理论的一般$ n_s-r $关系。如我们所示，可行的$ f（r）$重力理论可以分为两类模型，内容涉及其对运行频谱索引的预测。 $ r^2 $ -ATTRACTOR模型预测频谱索引在$ -10^{ - 3} <a_s <-10^{ - 4} $的范围内的运行，这将它们分类为大多数通货膨胀标量字段模型所属于的同一通用类别。我们提供了三种模型，为此我们详细验证了我们的主张。但是，存在可行的$ f（r）$重力模型，其光谱索引的运行范围$ -10^{ - 3} <a_s <-10^{ - 4} $，在某些情况下可能是正面的。我们还提出了一个$ r^2 $校正的标量字段模型，该模型还可以预测频谱索引在$ -10^{ - 3} <a_s <-10^{ - 4} $的范围内运行。对于我们研究的所有情况，我们没有发现最现象学上有趣的方案的证据，表明$ r <10^{ - 4} $和一个运行的$ a_s <-10^{ - 3} $，原则上可以实现。
In this work we shall provide a model-independent general calculation of the running of the spectral index for vacuum $F(R)$ gravities. We shall exploit the functional form of the spectral index and of the tensor-to-scalar ratio in order to present a general $n_s-r$ relation for vacuum $F(R)$ gravity theories. As we show, viable $F(R)$ gravity theories can be classified to two classes of models regarding their prediction for the running spectral index. The $R^2$-attractor models predict a running of the spectral index in the range $-10^{-3}<a_s<-10^{-4}$, which classifies them in the same universality class that most inflationary scalar field models belong to. We provide three models of this sort, for which we verify our claims in detail. However there exist viable $F(R)$ gravity models with running of spectral index outside the range $-10^{-3}<a_s<-10^{-4}$ and in some cases it can be positive. We also present an $R^2$-corrected scalar field model, which also predicts a running of the spectral index in the range $-10^{-3}<a_s<-10^{-4}$. For all the cases we studied, we found no evidence for the most phenomenologically interesting scenario of having $r<10^{-4}$ and a running $a_s<-10^{-3}$, which in principle could be realized.
