Asymptotic safety of gravity, the Higgs boson mass and beyond the Standard Model physics

There are many hints that gravity is asymptotically safe. The inclusion of gravitational corrections can result in the ultraviolet fundamental Standard Model and constrain the Higgs mass to take exactly one value, which can be calculated. Taking into account the current top quark mass measurements this calculation gives Higgs mass $\sim131$ GeV, which is in disagreement with the current experimental measurement. \\ This article considers the predictions of the Higgs mass in two minimal Beyond Standard Model scenarios. One is the sterile quark axion model, while the other is the $U(1)_{B-L}$ gauge symmetry model introducing a new massive $Z'$ gauge boson. The inclusion of $Z'$ boson gives the prediction much closer to the observed value, while inclusion of sterile quark(s) gives only a slight effect.\\ Also a new, gravitational solution to the strong CP problem is discussed