Higgs inflation and the Palatini formulation of General Relativity

The Standard Model Higgs can be the inflaton, providing an attractively economical scenario. The core idea is simple, but there are complications both on the side of quantum corrections and gravity. I will discuss possibilities and problems due to such complications. In particular I will cover how the predictions of Higgs inflation depend on what is the correct formulation of general relativity: metric, Palatini or something else.