论文标题
$ f（r）$重力中的通货膨胀吸引子
Inflationary Attractors in $F(R)$ Gravity
论文作者
论文摘要
在这封信中，我们将证明可行的$ f（r）$重力可以分为两类的通货膨胀吸引子，即$ r^2 $吸引者或$α$ - 吸引者。为了证明这一点，我们将通过假设慢速滚动条件约束慢滚子索引的值，从而得出张量与尺度比率$ r $ $ r $ $ r $ $ r $和原始曲率的光谱指数，即$ r-n_s $之间的关系。如我们所示，张量比比率与原始曲率扰动的光谱指数之间的关系具有$ r \ simeq \ frac {48（1-n_s）^2} {（1-n_s）^2} {（4-x）{（4-x）^2} $，在$ x $中，$ x $ compor $ x $ contriv and cartir cartit cartir and cartitiation $ x $ fation and Itition $ f（r）是$ e $ foldings number $ n $的函数，也可能是各种$ f（r）$重力模型的免费参数的函数。对于具有与观察数据兼容的频谱索引兼容的$ f（r）$重力，它们也属于$ r^2 $ type的吸引子，具有$ r \ r \ sim 3（1-n_s）^2 $，这些都是可行的。此外，如果$ x $在特定范围内采用较大的值，并且对于给定的$ f（r）$重重是恒定的，则结果$ r-n_s $关系具有$ r \ sim3α（1-n_s）^2 $的形式，其中$α$是常数。因此，我们得出的结论是，可行的$ f（r）$重重可以分为两种限制类型的$ r-n_s $关系，一种与$ x $中的$ r^2 $型号相同，一种类似于$ f（r）$ f（r）$ f（r）$ f（r）$ f（r）$ f（r）$ f（r）$ farvemity型号。最后，我们还讨论了$ x $不是恒定的案例。
In this letter we shall demonstrate that the viable $F(R)$ gravities can be classified mainly into two classes of inflationary attractors, either the $R^2$ attractors or the $α$-attractors. To show this, we shall derive the most general relation between the tensor-to-scalar ratio $r$ and the spectral index of primordial curvature perturbations $n_s$, namely the $r-n_s$ relation, by assuming that the slow-roll condition constrains the values of the slow-roll indices. As we show, the relation between the tensor-to-scalar ratio and the spectral index of the primordial curvature perturbations has the form $r\simeq \frac{48 (1-n_s)^2}{(4-x)^2}$, where the dimensionless parameter $x$ contains higher derivatives of the $F(R)$ gravity function with respect to the Ricci scalar, and it is a function of the $e$-foldings number $N$ and may also be a function of the free parameters of the various $F(R)$ gravity models. For $F(R)$ gravities which have a spectral index compatible with the observational data and also yield $x\ll 1$, these belong to the $R^2$-type of attractors, with $r\sim 3 (1-n_s)^2$, and these are viable theories. Moreover, in the case that $x$ takes larger values in specific ranges and is constant for a given $F(R)$ gravity, the resulting $r-n_s$ relation has the form $r\sim 3 α(1-n_s)^2$, where $α$ is a constant. Thus we conclude that the viable $F(R)$ gravities may be classified into two limiting types of $r-n_s$ relations, one identical to the $R^2$ model at leading order in $x$, and one similar to the $α$-attractors $r-n_s$ relation, for the $F(R)$ gravity models that yield $x$ constant. Finally, we also discuss the case that $x$ is not constant.
