Electromagnetism with dimension-five operators

TL;DR

This paper derives the most general Lorentz-violating electromagnetic Lagrangian with dimension-five operators in curved spacetime, exploring implications for cosmic magnetic fields and birefringence, and identifying new CPT-odd terms affecting dispersion relations.

Contribution

It introduces a comprehensive Lorentz-violating electromagnetic Lagrangian with dimension-five operators and analyzes their effects in cosmological contexts, including new CPT-odd terms.

Findings

Identification of a new CPT-odd term affecting dispersion relations.

Analysis of cosmic magnetic field generation during inflation.

Implications for cosmic birefringence and Lorentz violation.

Abstract

We derive, in curved spacetime, the most general Lorentz-violating electromagnetic Lagrangian containing dimension-five operators with one more derivative than the Maxwell term in the hypothesis that Lorentz symmetry is broken by a background four-vector $n_\mu$. We then study, for the case of isotropic $n_\mu$, the generation of cosmic magnetic fields at inflation and cosmic birefringence. In the limiting case of Minkowski spacetime, we find that other than the CPT-odd Myers-Pospelov term, there exists another CPT-odd term that gives rise to nontrivial dispersion and constitutive relations.