在斯塔罗宾斯基模型中，预期的引力波背景振幅是多少？
What is the amplitude of the Gravitational Waves background expected in the Starobinsky model ?
摘要：
Starobinski在1979年提出的暴胀模型预言了在标量谱指数为$n_S=0.965$的情况下，原初引力波的谱振幅为$r=0.0037$。该振幅目前被用作未来CMB实验设计中的目标值，最终目标是在超过五个标准差的情况下测量该振幅。在这里，我们评估如何稳定的$r$考虑$n_S$和$Λ$ CDM的假设实验的不确定性的Starobinski模型的预测。我们还考虑了暴胀模型，其中Starobinsky作用量中的PDMATHAMR项被推广为指数PDMATHAMT接近于1的$R^{2p}$项。我们发现，当前数据将$r>0.0013$的下限设定为$95 \%$ C. L。对于经典的Starobinski模型，并且还预测在$dn/dlnk=-0.0006_{-0.0001}^{+0.0002}$范围内的大于三个标准偏差处的标量指数的运行不同于零。因此，在Starobinski方案中可能存在$r\sim0.001$级的引力波，并且未来的CMB任务将无法像LiteBIRD和CMB-S4那样清楚地探测到它。当假设更一般的$R^{2p}$膨胀时，我们发现$r$没有预期的下限，并且运行与零一致。我们发现，目前的数据能够在$95\%$ C.L.对$R^{2p}$模型的索引进行严格的约束。即$p= 0.99^{+0.02}_{-0.03}$。
英文摘要：
The inflationary model proposed by Starobinski in 1979 predicts an amplitude of the spectrum of primordial gravitational waves, parametrized by the tensor to scalar ratio, of $r=0.0037$ in case of a scalar spectral index of $n_S=0.965$. This amplitude is currently used as a target value in the design of future CMB experiments with the ultimate goal of measuring it at more than five standard deviations. Here we evaluate how stable are the predictions of the Starobinski model on $r$ considering the experimental uncertainties on $n_S$ and the assumption of $Λ$CDM. We also consider inflationary models where the $R^2$ term in Starobinsky action is generalized to a $R^{2p}$ term with index $p$ close to unity. We found that current data place a lower limit of $r>0.0013$ at $95 \%$ C.L. for the classic Starobinski model, and predict also a running of the scalar index different from zero at more than three standard deviation in the range $dn/dlnk=-0.0006_{-0.0001}^{+0.0002}$. A level of gravitational waves of $r\sim0.001$ is therefore possible in the Starobinski scenario and it will not be clearly detectable by future CMB missions as LiteBIRD and CMB-S4. When assuming a more general $R^{2p}$ inflation we found no expected lower limit on $r$, and a running consistent with zero. We found that current data are able to place a tight constraints on the index of $R^{2p}$ models at $95\%$ C.L. i.e. $p= 0.99^{+0.02}_{-0.03}$.
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