  Recent work has shown that non-local modifications of gravity involving terms
such as $m^2R\Box^{-2}R$ (and no cosmological constant) provide a
phenomenologically viable alternative to $\Lambda$CDM. We first discuss the
possibility that such non-local terms emerge in the far infrared from the
running of a coupling constant associated to the $R^2$ term in
higher-derivative gravity, which, depending on the UV completion of the theory,
can be asymptotically free in the ultraviolet and strongly coupled in the
infrared. In this scenario the mass scale $m$ of the non-local model emerges
from dimensional transmutation, similarly to $\Lambda_{\rm QCD}$ for strong
interactions, leading to a technically natural value and to a novel
understanding of the scale associated to dark energy. Motivated by these
findings, we then explore the possibility of generating strong infrared effects
in Einstein gravity, with no $R^2$ terms, as a consequence of the
higher-derivative term generated by the conformal anomaly.
