(In)equivalence of Metric-Affine and Metric Effective Field Theories

Abstract

In a geometrical approach to gravity the metric and the (gravitational) connection can be independent and one deals with metric-affine theories. We construct the most general action of metric-affine effective field theories, including a generic matter sector, where the connection does not carry additional dynamical fields. Among other things, this helps in identifying the complement set of effective field theories where there are other dynamical fields, which can have an interesting phenomenology. Within the latter set, we study in detail a vast class where the Holst invariant (the contraction of the curvature with the Levi-Civita antisymmetric tensor) is a dynamical pseudoscalar. In the Einstein-Cartan case (where the connection is metric compatible and fermions can be introduced) we also comment on the possible phenomenological role of dynamical dark photons from torsion and compute interactions of the above-mentioned pseudoscalar with a generic matter sector and the metric. Finally, we show that in an arbitrary realistic metric-affine theory featuring a generic matter sector the equivalence principle always emerges at low energies without the need to postulate it.

arXiv commentv3: matches published version, 31 pages, 1 figure

References in corpus (33)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• f(R) Theories Of Gravity
• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• f(R) theories
• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
• First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole
• General relativity as an effective field theory: The leading quantum corrections
• Coincident General Relativity
• Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory
• First Sagittarius A* Event Horizon Telescope Results. VI: Testing the Black Hole Metric
• Physical Aspects of the Space-Time Torsion
• Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action
• First Sagittarius A* Event Horizon Telescope Results. III: Imaging of the Galactic Center Supermassive Black Hole
• Introduction to Effective Field Theory
• Massless Gauge Bosons other than the Photon
• Palatini inflation in models with an $R^2$ term
• General Teleparallel Quadratic Gravity
• Universal Limits on Massless High-Spin Particles
• A New Class of Ghost and Tachyon Free Metric Affine Gravities
• The dynamics of metric-affine gravity
• On the equivalence of the Einstein-Hilbert and the Einstein-Palatini formulations of general relativity for an arbitrary connection
• Metric-Affine Gravity as an Effective Field Theory
• Palatini formulation of pure $R^2$ gravity yields Einstein gravity with no massless scalar
• The role of nonmetricity in metric-affine theories of gravity
• Auxiliary fields representation for modified gravity models
• Low-energy general relativity with torsion: a systematic derivative expansion
• Coupling Metric-Affine Gravity to a Higgs-Like Scalar Field
• Torsion Phenomenology at the LHC
• Revisiting the Stability of Quadratic Poincaré Gauge Gravity
• Matter matters in Einstein-Cartan gravity
• Different types of torsion and their effect on the dynamics of fields
• The Equivalence Principle in a Quantum World