Decoupling theorem and effective quantum gravity

This is a contribution to the memorial edition devoted to Professor Vladislav Gavrilovich Bagrov, who was my official adviser from the beginning of the undergraduate period to the end of PhD. The article mentions my two publications in Izvestia VUZov Fizika (Russian Physics Journal), where Vladislav Gavrilovich held the position of editor-in-chief. This paper is based on the recent lectures about decoupling in quantum gravity, given in ICTP-SAIFR in São Paulo and at the Estate Quantistica school in Scalea, Italy. After a brief and mainly qualitative review of the decoupling theorem in semiclassical gravity and the scalar fourth-derivative model of Antoniadis and Mottola, we explain what is the expected result for the physical beta functions in fourth-derivative quantum gravity and what should remain from these beta functions in the infrared range.