Programme

Abstract. Aside from philosophical interest, Lagrangians that contain higher time derivatives hold great interest for quantum gravity owing to the theorem of the late Kelly Stelle that adding fundamental Ricci-squared and Weyl-squared terms to the Hilbert action would result in a perturbatively renormalizable theory. The reason we still have a ``problem of quantum gravity'' is that the Weyl-squared term is not allowed. I explain why not, and hopefully debunk some of the confused and confusing literature on this subject. This talk is based on astro-ph/0601672, arXiv:1506.022, arXiv:2306.09596 and arXiv:2602.16190.