Backgrounds in gravitational effective field theory

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 included. The theoretical framework violations associated conceptual issues discussed, including transformations in curved approximately flat spacetimes, the treatment various types backgrounds, implications symmetry breaking, no-go constraints explicit violation Riemann geometry. Techniques presented construction effective operators, possible terms gravity, gauge, fermion, scalar sectors classified enumerated. Explicit expressions obtained containing dimension six or less action general relativity Standard Model particle physics. Special cases considered include Einstein-Maxwell limit with only coupling constants.