Inflation model building with an accurate measure of e-folding

TL;DR

This paper introduces an alternative framework for inflation model building that accurately measures e-folding using the inverse Hubble radius, avoiding common approximations and enabling exact analytical solutions.

Contribution

It proposes a new method using the inverse Hubble radius to precisely determine e-folding, improving upon the standard logarithmic measure in inflation models.

Findings

The new framework yields the correct number of e-foldings naturally.

An exactly solvable inflationary model is constructed.

Special cases reduce to known power-law inflation models.

Abstract

It has become standard practice to take the logarithmic growth of the scale factor as a measure of the amount of inflation, despite the well-known fact that this is only an approximation for the true amount of inflation required to solve the horizon and flatness problems. The aim of this work is to show how this approximation can be completely avoided using an alternative framework for inflation model building. We show that using the inverse Hubble radius as the key dynamical parameter, the correct number of e-folding arises naturally as a measure of inflation. As an application, we present an interesting model in which the entire inflationary dynamics can be solved analytically and exactly, and, in special cases, reduces to the familiar class of power-law models.