Higgs inflation is a well-motivated inflation model because of its compatibility with observations and minimality by utilizing the Standard Model Higgs with non-minimal coupling to gravity. However, this model becomes strongly-coupled during preheating, which jeopardizes the validity of predictions by this model. Many efforts have been paid to avoid this strong coupling issue by UV-extending the Higgs inflation. In this talk, I will discuss the one-loop correction to the Higgs inflation which generally induces a new scalar degree of freedom, the scalaron, that can play an important role in UV-extension of the original model, and the inflation dynamics in the presence of the scalaron. In particular, my discussion is based on the Higgs inflation in Einstein-Cartan gravity which is a general setup that includes two commonly discussed versions of Higgs inflation, i.e. the metric and the Palatini Higgs inflation.