用光谱指数和再加热温度约束$f(R)$模型
Constraining $f(R)$ model through spectral indices and reheating temperature
摘要：
我们研究了一种形式的$ f(R) = {R^{1+δ}}/{R_c^δ}$和研究的可行性模型的膨胀在约旦和爱因斯坦框架。利用膨胀率和再加热温度的功率谱指标对该模型进行了进一步分析。在暴胀演化过程中，该模型预测的$δ$参数值非常接近1（$δ=0.98$），而在$δ=0.98$的再加热温度$T_{re} \sim 10^{17}$ GeV与标准的暴胀和观测方法是一致的。在此模型的框架下，我们计算了最小耦合标量场的慢滚参数。发现标量谱指数和张量标量比的值与最近的观测数据非常接近，包括普朗克2018年发布的数据。利用标量谱指数、张量标量比和再加热温度证明了当$δ\sim 1 $时，Jordan和Einstein框架是等价的.
英文摘要：
We investigate a form of $ f(R) = {R^{1+δ}}/{R_c^δ}$ and study the viability of the model for inflation in the Jordan and the Einstein frames. This model is further analysed by using the power spectrum indices of the inflation and the reheating temperature. During the inflationary evolution, the model predicts a value of $δ$ parameter very close to one ($δ=0.98$), while the reheating temperature $T_{re} \sim 10^{17}$ GeV at $δ=0.98$ is consistent with the standard approach to inflation and observations. We calculate the slow roll parameters for the minimally coupled scalar field within the framework of our model. It is found that the values of the scalar spectral index and tensor-to-scalar ratio are very close to the recent observational data, including those released by Planck 2018. We also show that the Jordan and the Einstein frames are equivalent when $δ\sim 1 $ by using the scalar spectral index, tensor-to-scalar ratio and reheating temperature.
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