# Vector Galileon and inflationary magnetogenesis

## TL;DR

This paper introduces a novel higher derivative electromagnetic action during inflation that breaks conformal invariance, enabling the generation of primordial magnetic fields with scale-dependent strengths.

## Contribution

It proposes a new theoretical framework for inflationary magnetogenesis using a vector Galileon-like electromagnetic action that satisfies specific physical conditions.

## Key findings

- Generates significant magnetic fields at small wavelengths.
- Produces tiny magnetic fields at large wavelengths consistent with observations.
- Provides a unique approach to breaking conformal invariance during inflation.

## Abstract

Cosmological inflation provides the initial conditions for the structure formation. However, the origin of large-scale magnetic fields cannot be addressed in this framework. The key issue for this long-standing problem is the conformal invariance of the electromagnetic (EM) field in 4-D. While many approaches have been proposed in the literature for breaking conformal invariance of the EM action, here, we provide a completely new way of looking at the modifications to the EM action and generation of primordial magnetic fields during inflation. We explicitly construct a higher derivative EM action that breaks conformal invariance by demanding three conditions - theory be described by vector potential $A_\mu$ and its derivatives, Gauge invariance be satisfied, and equations of motion be linear in second derivatives of vector potential. The unique feature of our model is that appreciable magnetic fields are generated at small wavelengths while tiny magnetic fields are generated at large wavelengths that are consistent with current observations.