Quadratic gravity in \((2+1)\)D with a topological Chern-Simons term (Q2766234)

Quadratic \((2+1)\)-dimensional gravitational theory modified by a Chern-Simons term is considered and compared to its unmodified version. It is found that (i) the harmless massive scalar mode of the latter becomes a troublesome massive spin-0 ghost in the former case, while the massive spin-2 ghost of quadratic \((2+1)\) gravity is now replaced by two massive physical particles of spin 2, (ii) the light deflection does not have the wrong sign such as in the framework of three-dimensional quadratic gravity, and (iii) in quadratic Chern-Simons \((2+1)\) gravity, the nonrelativistic potential is well behaved and the massless excitation is non-propagating.