In this work we study the scalar power spectrum and the spectral index for the Starobinsky inflationary model using the phase integral method up-to third-order of approximation. We show that the semiclassical methods reproduce the scalar power spectrum for the Starobinsky model with a good accuracy, and the value of the spectral index compares favourably with observations. Also, we compare the results with the uniform approximation method and the second-order slow-roll approximation.

中文翻译：

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Starobinsky通胀模型的半经典分析

在这项工作中，我们使用相位积分法直至三阶逼近，研究了Starobinsky膨胀模型的标量功率谱和谱指数。我们表明，半经典方法可以很好地再现Starobinsky模型的标量功率谱，并且光谱指数的值与观测值相比具有优势。另外，我们将结果与均匀逼近法和二阶慢滚逼近相比较。