  We explore the possibility of a consistent cosmology based on the
gauge-fixing independent running of the gravitational and cosmological
constants ($G$ and $\Lambda$) in the framework of effective quantum gravity. In
particular, their running in this framework was found to satisfy $G \propto
\Lambda^4$. In the cosmological setting, the covariance of the theory provides
energy conservation relations, which are impossible to satisfy with the unique
scale parameter. However, by introducing the second sub-dominant scale
corresponding to the higher-loop corrections and higher-derivative terms, one
can close the system of equations for the running of parameters and arrive at
the consistent cosmological solutions. This approach yields a change in the
cosmological expansion history that affects the ratio of the Hubble parameter
today to the Hubble parameter at high redshift.
