Clocking the End of Cosmic Inflation

TL;DR

This paper introduces a new analytical method that significantly reduces uncertainties in determining the timing of horizon exit during inflation, improving the precision of cosmological predictions beyond the slow-roll approximation.

Contribution

A novel analytical approach that enhances the accuracy of inflationary horizon exit timing estimates, surpassing traditional slow-roll approximation limitations.

Findings

Reduces uncertainty on e-folds to less than a tenth of an e-fold.

Improves the precision of observable predictions for cosmic inflation.

Addresses limitations of the slow-roll approximation near inflation's end.

Abstract

Making observable predictions for cosmic inflation requires determining when the wavenumbers of astrophysical interest today exited the Hubble radius during the inflationary epoch. These instants are commonly evaluated using the slow-roll approximation and measured in e-folds $\Delta N=N-N_\mathrm{end}$, in reference to the e-fold $N_\mathrm{end}$ at which inflation ended. Slow roll being necessarily violated towards the end of inflation, both the approximated trajectory and $N_\mathrm{end}$ are determined at, typically, one or two e-folds precision. Up to now, such an uncertainty has been innocuous, but this will no longer be the case with the forthcoming cosmological measurements. In this work, we introduce a new and simple analytical method, on top of the usual slow-roll approximation, that reduces uncertainties on $\Delta N$ to less than a tenth of an e-fold.