Scaling solution for field-dependent gauge couplings in quantum gravity

Quantum gravity can determine the dependence of gauge couplings in a scalar field, which is related to possible fifth forces and time varying fundamental “constants”. This prediction based on scaling solution functional flow equations. For momenta below field-dependent Planck mass quantum scale invariant standard model emerges as an effective low energy theory. small non-zero value infrared cutoff time-variation or apparent violations equivalence principle turn out be negligibly for present cosmological epoch, unless some further symmetry violation beyond comes into play. More sizable effects are expected during nucleosynthesis before. Scaling solutions relate field renormalization scale. We find asymptotically free coupled gravity, while grand unified models safe with values at ultraviolet fixed point. The metric yields restrictions building, limiting number scalars theories.