Chern-Simons inspired massive gravity

In this work, we propose a new <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mn>2</a:mn> <a:mo>+</a:mo> <a:mn>1</a:mn> </a:mrow> </a:math> theory of gravity. We start with a modification of Chern-Simons <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mn>2</c:mn> <c:mo>+</c:mo> <c:mn>1</c:mn> </c:mrow> </c:math> gravity. By introducing a vector field <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi mathvariant="normal">Φ</e:mi> </e:math> to the usual composition of the vierbein and connection, we derive a new action that includes the Einstein-Hilbert term, a cosmological constant, and a polynomial term for the vector field. This allows us to write a Chern-Simons-inspired massive gravity that generalizes new massive gravity. After solving the polynomial function, the action can be rewritten as a Born-Infeld-type action. Moreover, we show that the second-order expansion of this action is equivalent to new massive gravity. We explore solutions to the theory and show that it has a Bañados-Teitelboim-Zanelli solution with an effective cosmological constant in terms of the parameters of the theory, global Lifshitz space-times as well as regular Lifshitz black holes, and asymptotically locally flat black holes. Furthermore, we study the decoupling limit of the theory, showing that it contains the quartic Galileon in addition to the cubic Galileon that is characteristic of new massive gravity.