Backgrounds in gravitational effective field theory

Abstract

Effective field theories describing gravity coupled to matter are investigated, allowing for operators of arbitrary mass dimension. Terms violating local Lorentz and diffeomorphism invariance while preserving internal gauge symmetries are included. The theoretical framework for violations of local Lorentz and diffeomorphism invariance and associated conceptual issues are discussed, including transformations in curved and approximately flat spacetimes, the treatment of various types of backgrounds, the implications of symmetry breaking, and the no-go constraints for explicit violation in Riemann geometry. Techniques are presented for the construction of effective operators, and the possible terms in the gravity, gauge, fermion, and scalar sectors are classified and enumerated. Explicit expressions are obtained for terms containing operators of mass dimension six or less in the effective action for General Relativity coupled to the Standard Model of particle physics. Special cases considered include Einstein-Maxwell effective field theories and the limit with only scalar coupling constants.

Hamiltonian formulation of an effective modified gravity with nondynamical background fields

“…The most recent article [39] rests on a better understanding of Lorentz violation in gravity acquired since the base of the gravitational SME was laid in [32]. It widely extends the findings in [32] and introduces additional concepts such as global local Lorentz transformations and manifold Lorentz transformations that are combinations of diffeomorphisms and local Lorentz transformations.…”

“…To incorporate these concepts into the SME language, a generic background field in a curved spacetime manifold M can have both contributions defined in a spacetime frame and contributions given in a local inertial reference frame. A gravitational version of the SME has been put forward in a series of papers [32][33][34][35][36][37][38][39] to study these aspects. The spacetime manifold itself is described by the metric tensor g µν and formal transitions between a spacetime frame and a local inertial frame are provided by vierbeins e a µ .…”

“…An almost flat spacetime setting, which is sufficient for various studies in practice such as propagating gravitational waves [35,38] or modified dispersion relations in linearized gravity [40], is also introduced. Therefore, [39] provides many additional possibilities of how to construct terms leading to observable puregravity effects that are not in accordance with GR. By employing a powerful notation, an infinite number of such terms covering the mass dimensions ≤ 8 is stated.…”

Non-Minimal Lorentz Violation in Macroscopic Matter

“…) a , and using the product identity derived in Appendix A, we can expand (33) in spherical-harmonic tensors. Combining the result with (5) gives the change in the spherical coefficients for Lorentz violation.…”

“…We can therefore safely neglect the effects of minimal Lorentz violations in the pure-photon sector of the SME. We will also neglect violations in electromagnetic interactions [31,32], matter-gravity couplings [17,33,34], and non-minimal violations in photons [13]. Including these would be of interest, but would complicate the analysis.…”