Introduction to the number of $e$-folds in slow-roll inflation

TL;DR

This paper provides a clear, pedagogical overview of the concept of the number of e-folds in slow-roll inflation, clarifying different definitions and their importance for inflationary predictions.

Contribution

It clarifies the distinctions between various notions of e-folds and discusses their proper application in inflationary cosmology.

Findings

Different definitions of e-folds are distinguished and explained.

Proper application of e-folds is crucial for accurate inflationary predictions.

The review emphasizes the role of e-folds as a time variable and a key parameter.

Abstract

In this review, a pedagogical introduction to the concepts of slow-roll inflationary Universe and number of $e$-folds is provided. In particular, the differences between the basic notion of number of $e$-folds ($N_e$), total number of $e$-folds ($N_T$) and number of $e$-folds before the end of inflation ($N$), are outlined. The proper application of the number of $e$-folds before the end of inflation is discussed both as a time-like variable for the scalar field evolution and as a key parameter for computing inflationary predictions.