Carrollian limit of quadratic gravity

In this talk, I will summarize the results on the Carrollian limit of Stelle’s quadratic curvature gravity. Naturally, the obtained Carrollian theories depend on the dependencies of the parameters in the action on the speed of light c. If we focus on the leading and the subleading orders of the expansion in c, we find that there are four inequivalent Carrollian theories that are sensible modifications of GR. Imposing conditions on the parameters to remove tachyons, we end up with a classification of Carrollian theories according to their leading order and next to leading order actions. All modify GR with quartic terms of the second fundamentalform.