Emergent Gravity, Violated Relativity and Dark Matter

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.