Solution for cosmological observables in the Starobinsky model of inflation

Abstract

AbstractThis 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 $$n_s$$ 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 $$\omega _{re}$$ ω re at the end of reheating. An equation linking inflation with reheating is established, which is solved for the spectral index $$n_s$$ n s . Using consistency relations of the model, we determine the other observables while the number of e-folds during inflation $$N_k$$ N k , and the number of e-folds during reheating $$N_{re}$$ N re are determined by their respective formulas involving $$n_s$$ 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.