Einstein-Cartan formulation of Chern-Simons Lorentz-violating gravity

Abstract

We consider a modification of the standard Einstein theory in four dimensions, alternative to R. Jackiw and S.-Y. Pi, Phys. Rev. D 68, 104012 (2003), since it is based on the first-order (Einstein-Cartan) approach to General Relativity, whose gauge structure is manifest. This is done by introducing an additional topological term in the action which becomes a Lorentz-violating term by virtue of the dependence of the coupling on the space-time point. We obtain a condition on the solutions of the Einstein equations, such that they persist in the deformed theory, and show that the solutions remarkably correspond to the classical solutions of a collection of independent 2 + 1-d (topological) Chern-Simons gravities. Finally, we study the relation with the standard second-order approach and argue that they both coincide to leading order in the modulus of the Lorentz-violating vector field.

Probing the effects of Lorentz-symmetry violating Chern-Simons and Ricci-Cotton terms in higher derivative gravity

“…A broad review on LV CS gravity is given in [9]. For further discussion, see [10][11][12][13][14][15][16][17][18][19].…”

Nonminimal couplings, gravitational waves, and torsion in Horndeski’s theory

“…Known results for the torsionless Horndeski theory encompass from cosmological models to black hole solutions. In the torsional Horndeski setting here presented, such solutions might persist [15,17] if one uplifts them in a consistent manner. This means, in particular, that the Riemann curvature and the scalar field should be the same as in the torsionless theory.…”

“…• The cosmological implications of Horndeski's theory have been studied only on particular cases (see, e.g., Refs. [15,17,18,21]).…”

“…They may be detectable in cosmological scenarios [10] and in theories that go beyond ECSK in four dimensions (see, e.g., Refs. [11][12][13][14][15][16][17][18][19][20][21][22][23][24]).…”

“…Several authors (see, e.g., Refs. [15,17,18,21]) have studied the consequences of including in the action a term that is the product of a scalar field and the Euler four-form density,…”