  We compute the effective potential for scalar fields in asymptotically safe
quantum gravity. A scaling potential and other scaling functions generalize the
fixed point values of renormalizable couplings. The scaling potential takes a
non-polynomial form, approaching typically a constant for large values of
scalar fields. Spontaneous symmetry breaking may be induced by non-vanishing
gauge couplings. We strengthen the arguments for a prediction of the ratio
between the masses of the top quark and the Higgs boson. Higgs inflation in the
standard model is unlikely to be compatible with asymptotic safety. Scaling
solutions with vanishing relevant parameters can be sufficient for a realistic
description of particle physics and cosmology, leading to an asymptotically
vanishing ''cosmological constant" or dynamical dark energy.
