Conformal symmetry and nonlinear extensions of nonlocal gravity

Understand

We study two nonlinear extensions of the nonlocal $R\,\Box^{-2}R$ gravity theory.

• We extend this theory in two different ways suggested by conformal symmetry, either replacing $\Box^{-2}$ with $(-\Box + R/6)^{-2}$, which is the operator that enters the action for a conformally-coupled scalar field, or replacing $\Box^{-2}$ with the inverse of the Paneitz operator, which is a four-derivative operator that enters in the effective action induced by the conformal anomaly.
• We show that the former modification gives an interesting and viable cosmological model, with a dark energy equation of state today $w_{\rm DE}\simeq -1.01$, which very closely mimics $\Lambda$CDM and evolves asymptotically into a de Sitter solution.
• The model based on the Paneitz operator seems instead excluded by the comparison with observations.