Abstract
The nonlinear affine Goldstone model of the emergent gravity, built on the nonlinearly realized/ hidden affine symmetry, is concisely revisited. Beyond General Relativity, the explicit violation of general invariance/relativity, under preserving general covariance, is exposed. Dependent on a nondynamical affine connection, a generally covariant second-order effective Lagrangian for metric gravity is worked out, with the general relativity violation and the gravitational dark matter serving as the signatures of emergence.
Highlights
It is widely accepted nowadays that General Relativity (GR) may be just an effective field theory of gravity to be superseded at the high energies by a more fundamental/underlying theory
The model is proposed as a prototype for the emergent gravity and space-time, with the GR violation and the gravitational dark matter (DM) serving as the signatures of emergence
The most general second-order generally covariant effective Lagrangian for the emergent metric gravity is given by Equation (17), with13 ( ) L0 = 2Λ − R gμν, Γλμν, ∆L1 = g μν Bμκκ Bνλλ
Summary
It is widely accepted nowadays that General Relativity (GR) may be just (a piece of) an effective field theory of gravity to be superseded at the high (conceivably, as high as the Planck scale) energies by a more fundamental/underlying theory. Being based on a nonlinearly realized/hidden symmetry, remaining linear on an unbroken subgroup, such a model could encounter in a concise manner for the spontaneously/dynamically broken symmetries of the fundamental theory. One might naturally expect that in the quest for an underlying theory of gravity GR should first be substituted by a nonlinear model As such a model for gravity, aimed principally at reconstructing GR, there was originally proposed the model based on the nonlinearly realized/hidden affine symmetry, remaining linear on the unbroken Poincare subgroup [5] [6]2. At that, reproducing GR the model may well include the GR violation [9]3 To this end, one should envisage in a field theory two kinds of fields—the dynamical/relative and nondynamical/absolute ones—and, respectively, two kinds of the diffeomorphism symmetries. Appendix B presents a short compendium of conventions and notations
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