The Scale Factor Potential Approach to Inflation

TL;DR

This paper introduces the scale factor potential as a new, model-independent method to analyze inflation, allowing for direct determination of its end and expressing observables in terms of the e-folding number, leading to potentials consistent with observations.

Contribution

It presents the scale factor potential approach for inflation analysis, enabling direct determination of inflation end and expressing observables via the e-folding number, with new scalar potentials matching observational data.

Findings

The scale factor potential allows immediate identification of inflation end.

Expressing inflationary observables in terms of the e-folding number simplifies analysis.

Constructed scalar potentials achieve spectral index and tensor-to-scalar ratio consistent with observations.

Abstract

We propose a new approach to investigate inflation in a model-independent way, and in particular to elaborate the involved observables, through the introduction of the "scale factor potential". Through its use one can immediately determine the inflation end, which corresponds to its first (and global) minimum. Additionally, we express the inflationary observables in terms of its logarithm, using as independent variable the e-folding number. As an example, we construct a new class of scalar potentials that can lead to the desired spectral index and tensor-to-scalar ratio, namely $n_s \approx 0.965$ and $r \sim 10^{-4}$ for 60 $e$-folds, in agreement with observations.