Dark energy and dimensional transmutation in $R^2$ gravity

Abstract

Recent work has shown that non-local modifications of gravity involving terms such as $m^{2}R{\square }^{-2}R$ (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 ${\Lambda }_{\mathrm{QCD}}$ 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.

34 pages; v3: significant conceptual improvements

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• Non-locality and late-time cosmic acceleration from an ultraviolet complete theory
• Quantum gravity of Kerr-Schild spacetimes and the logarithmic correction to Schwarzschild black hole entropy