Solution for cosmological observables in the Starobinsky model of inflation

Abstract: This paper focuses on the Starobinsky model of inflation. 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. We establish an equation that connects inflation and reheating, which can be solved for the spectral index $n_s$. Using consistency relations of the model, we determine the other observables, the number of $e$-folds during inflation $N_k$, and the number of $e$-folds during reheating $N_{re}$. The impact of reheating on inflation is explored by constraining the equation of state parameter $\omega_{re}$ at the end of reheating. 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.