Is asymptotically Weyl-invariant gravity viable?

We explore the cosmological viability of a theory gravity defined by Lagrangian $f(\mathcal{R})=\mathcal{R}^{n\left(\mathcal{R}\right)}$ in Palatini formalism, where $n\left(\mathcal{R}\right)$ is dimensionless function scalar curvature $\mathcal{R}$ that interpolates between general relativity when $n\left(\mathcal{R}\right)=1$ and locally scale-invariant superficially renormalizable $n\left(\mathcal{R}\right)=2$. refer to this model as asymptotically Weyl-invariant (AWIG). analyse perhaps simplest possible implementation AWIG. A phase space analysis yields three fixed points with effective equation states corresponding de Sitter, radiation matter-dominated phases. An deceleration parameter suggests our consistent an early late period accelerated cosmic expansion, intermediate decelerated expansion. show contains no obvious singularities. Therefore, AWIG appears be cosmologically viable, at least for simple explored.