This paper focuses on the Starobinsky model of inflation in the Einstein frame. We derive solutions for various cosmological observables, such as the scalar spectral index \(n_s\), the tensor-to-scalar ratio r and their runnings, as well as the number of e-folds of inflation, reheating, and radiation, with minimal assumptions. The impact of reheating on inflation is explored by constraining the equation of state parameter \(\omega _{re}\) at the end of reheating. An equation linking inflation with reheating is established, which is solved for the spectral index \(n_s\). Using consistency relations of the model, we determine the other observables while the number of e-folds during inflation \(N_k\), and the number of e-folds during reheating \(N_{re}\) are determined by their respective formulas involving \(n_s\). We find remarkable agreement between the Starobinsky model and current measurements of the power spectrum of primordial curvature perturbations and the present bounds on the spectrum of primordial gravitational waves.

本文重点讨论爱因斯坦框架下的斯塔罗宾斯基暴胀模型。我们推导出各种宇宙学可观测量的解，例如标量谱指数\(n_s\)、张量标量比r及其运行，以及膨胀、再加热和辐射的e倍数，其中最小的假设。通过约束再加热结束时的状态参数方程\(\omega _{re}\)来探讨再加热对通货膨胀的影响。建立了将膨胀与再加热联系起来的方程，并求解了光谱指数\(n_s\)。利用模型的一致性关系，我们确定了其他可观测量，而膨胀期间的e折叠次数\(N_k\)和再加热期间的e折叠次数\(N_{re}\)由各自的公式确定涉及\(n_s\)。我们发现斯塔罗宾斯基模型和当前对原初曲率扰动功率谱的测量以及原初引力波谱的当前界限之间存在显着的一致性。