Two gravitationally Chern-Simons terms are too many

TL;DR

The paper demonstrates that adding a second gravitational Chern-Simons term to topological massive gravity results in a non-physical model with no positive energy spectrum, indicating such a double CS-action is not physically relevant.

Contribution

It shows that incorporating two gravitational Chern-Simons terms leads to a non-viable model due to energy positivity issues, clarifying limitations of such modifications.

Findings

The model contains two massive spin-2 excitations.

The light-front energy is not semidefinite positive.

The double CS-action lacks physical relevance.

Abstract

It is shown that topological massive gravity augmented by the triadic gravitational Chern-Simons first order term is a curved a pure spin-2 action. This model contains two massive spin-2 excitations. However, since its light-front energy is not semidefinite positive, this double CS-action does not have any physical relevance.In other words, topological massive gravity cannot be spontaneously broken down by the presence of the triadic CS term.