Asymptotic safety of higher derivative quantum gravity non-minimally coupled with a matter system

Understand

We study asymptotic safety of models of the higher derivative quantum gravity with and without matter.

• The beta functions are derived by utilizing the functional renormalization group, and non-trivial fixed points are found.
• It turns out that all couplings in gravity sector, namely the cosmological constant, the Newton constant, and the $R^2$ and $R_{\mu\nu}^2$ coupling constants, are relevant in case of higher derivative pure gravity.
• For the Higgs-Yukawa model non-minimal coupled with higher derivative gravity, we find a stable fixed point at which the scalar-quartic and the Yukawa coupling constants become relevant.