Conformal symmetry and nonlinear extensions of nonlocal gravity

TL;DR

This paper explores two conformally-inspired nonlinear extensions of nonlocal gravity, finding one model that closely mimics dark energy behavior consistent with observations and another that appears observationally excluded.

Contribution

It introduces and analyzes two novel conformal symmetry-based nonlinear modifications of nonlocal gravity, assessing their cosmological viability and observational consistency.

Findings

The conformally-coupled scalar operator extension yields a viable dark energy model.

The Paneitz operator extension is inconsistent with observational data.

Nonlocal models can interpolate between inflation and late-time acceleration.

Abstract

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. We also review some issues about the causality of nonlocal theories, and we point out that these nonlocal models can be modified so to nicely interpolate between Starobinski inflation in the primordial universe and accelerated expansion in the recent epoch.