  Scale-dependence is a common feature to all effective models of quantum
gravity. In this paper, a cosmological model based on the scale-dependent
scenario of gravity is presented. It is argued that such models, where the
scale-dependence appears as a correction to the classical $\Lambda$CDM
evolution, have the potential of addressing the tensions between early and late
time measurements of $H_0$. After defining criteria to parametrize this
tension, we perform a numerical scan over the parameter space of the
scale-dependent model, subject to these criteria. In this analysis, it is found
that, indeed, the tension can be released.
