Precision Inflationary Predictions: Impact of Accurate End-of-Inflation Dynamics

TL;DR

This paper systematically assesses how precise modeling of end-of-inflation dynamics and higher-order slow-roll corrections affect inflationary predictions, especially the spectral index, with implications for future CMB observations.

Contribution

It introduces a framework for incorporating accurate end-of-inflation dynamics and higher-order corrections into inflationary predictions, specifically applied to the Starobinsky model.

Findings

Improved end-of-inflation modeling shifts $n_s$ by about 10^{-3}.

Higher-order slow-roll corrections refine $n_s$ predictions by approximately 4×10^{-4}.

Total shift in $n_s$ can reach around 1.2×10^{-3} within reheating uncertainties.

Abstract

The precision era of cosmology demands accurate theoretical predictions from inflationary models. In quantitative reheating analyses, inflationary observables depend sensitively on the number of e-folds between horizon exit and the end of inflation, $N_k$, whose determination relies on slow-roll approximations near the end of inflation. Since inflation ends when the first slow-roll parameter reaches unity, even modest inaccuracies in this approximation can shift the end of inflation and thereby alter $N_k$, leading to modifications in predicted observables -- including those evaluated at leading-order. While such effects are implicit in standard treatments, their quantitative impact on observable constraints has not been systematically assessed. In this work, we first re-evaluate leading-order slow-roll predictions using an improved determination of $N_k$ within a simple quantitative reheating framework, and then incorporate higher-order slow-roll corrections consistently with the revised background evolution. Applying this framework to the Starobinsky model, we find that improved end-of-inflation dynamics alone can induce shifts of order $\Delta n_s \sim 10^{-3}$, while higher-order slow-roll corrections provide additional refinements at the $\sim 4 \times 10^{-4}$ level. The cumulative effect yields a maximum shift of $\Delta n_s \sim 1.2 \times 10^{-3}$ within the allowed reheating range. To our knowledge, this is the first systematic decomposition of end-of-inflation corrections and their individual contributions to $n_s$ in the Starobinsky model, with implications for model discrimination in next-generation CMB surveys. These results demonstrate that an accurate determination of the end of inflation is essential for precision tests of inflationary models.