GEFF: The Gradient Expansion Formalism Factory - A tool for inflationary gauge-field production

Abstract: The GEFF - the Gradient Expansion Formalism Factory - is a new Python package designed to study gauge-field production during inflation. The package provides a framework to implement and use the gradient expansion formalism (GEF), a numerical technique devised to study the nonlinear dynamics associated with inflationary gauge-field generation. The GEF has already been applied in the context of axion inflation, and with the GEFF package, one can build on these results. The GEFF gives users access to ready-to-use model files for two scenarios of axion inflation: pure axion inflation, with the inflaton coupled to a pure Abelian gauge sector, and fermionic axion inflation, which assumes that the Standard Model (SM) hypercharge field is coupled to the inflaton, resulting in the production SM fermions via the Schwinger effect. The GEFF provides the user with methods to solve GEF equations, including an integrated error estimator and self-correction algorithm. Furthermore, users can implement their own GEF models, e.g., variations of axion inflation or related scenarios. The package also comes with tools to study the production of primordial gravitational waves induced by gauge fields. This is a starting guide for the GEFF, providing a high-level introduction to the GEF, installation instructions, and the basics for using this package.