Sigmoidal Inflation

TL;DR

This paper introduces a new inflationary cosmological model using a logistic generating function, deriving key observables exactly without slow roll approximation, and aligning well with Planck data.

Contribution

The paper presents a novel inflationary model constructed with the Ivanov-Salopek-Bond method and logistic function, providing exact calculations of inflationary parameters.

Findings

Scalar spectral index and tensor-to-scalar ratio match Planck measurements.

Reheating predicts high temperatures with a small number of e-folds.

Model's predictions are consistent with observational bounds.

Abstract

In this paper we present a new cosmological inflationary model which is constructed using the Ivanov-Salopek-Bond method with a logistic generating function. We derive the inflationary observables as well as the duration and temperature of the subsequent reheating epoch of our model exactly, with no need to recur to the slow roll approximation. The obtained scalar spectral index and tensor-to-scalar ratio of perturbations fall comfortably within the range of the measurements presented by the Planck collaboration. On the other hand, for the reheating era, our model predicts a relatively small number of e-folds and thus high temperatures, still within range of Planck's bounds.