  The effective action in quantum general relativity is strongly dependent on
the gauge-fixing and parametrization of the quantum metric. As a consequence,
in the effective approach to quantum gravity, there is no possibility to
introduce the renormalization-group framework in a consistent way. On the other
hand, the version of effective action proposed by Vilkovisky and DeWitt does
not depend on the gauge-fixing and parametrization off-shell, opening the way
to explore the running of the cosmological and Newton constants as well as the
coefficients of the higher-derivative terms of the total action. We argue that
in the effective framework the one-loop beta functions for the zero-, two- and
four-derivative terms can be regarded as exact, that means, free from
corrections coming from the higher loops. In this perspective, the running
describes the renormalization group flow between the present-day Hubble scale
in the IR and the Planck scale in the UV.
