Solution for cosmological observables in the Starobinsky model of inflation

TL;DR

This paper derives solutions for key cosmological observables within the Starobinsky inflation model, linking inflation and reheating processes, and confirms the model's consistency with current observational data.

Contribution

It provides a comprehensive analytical framework connecting inflation and reheating in the Starobinsky model, including new equations and constraints on observables.

Findings

Good agreement with current measurements of primordial power spectrum

Constraints on reheating equation of state parameter

Consistency with bounds on primordial gravitational waves

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.