It's Hard to Learn How Gravity and Electromagnetism Couple

Abstract

We construct the most general effective Lagrangian coupling gravity and electromagnetism up to mass dimension 6 by enumerating all possible non-minimal coupling terms respecting both diffeomorphism and gauge invariance. In all, there are only two unique terms after field re-definitions; one is known to arise from loop effects in QED while the other is a parity violating term which may be generated by weak interactions within the standard model of particle physics. We show that neither the cosmological propagation of light nor, contrary to earlier claims, solar system tests of General Relativity are useful probes of these terms. These non-minimal couplings of gravity and electromagnetism may remain a mystery for the foreseeable future.

9 pages. Minor corrections made. To appear in Phys. Rev. D

References in corpus (2)

• Constraints on CPT violation from WMAP three year polarization data: a wavelet analysis
• Limits on Cosmological Birefringence from the Ultraviolet Polarization of Distant Radio Galaxies

Cited by in corpus (7)

• The Speed of Gravity
• Lifshitz scalar fields: one loop renormalization in curved backgrounds
• Nonlinear electrodynamics and CMB polarization
• Strong Lensing and Nonminimally Coupled Electromagnetism
• Comparing metric and Palatini approaches to vector Horndeski theory
• On the Non-Minimal Coupling of Magnetic Fields with Gravity in Schwarzschild Spacetime
• Bounds on Parity Violation In the Cosmological Redshift