Fixed Points of Quantum Gravity and the Dimensionality of the UV Critical Surface

Understand

We study quantum effects in higher curvature extensions of general relativity using the functional renormalisation group.

• New flow equations are derived for general classes of models involving Ricci scalar, Ricci tensor, and Riemann tensor interactions.
• Our method is applied to test the asymptotic safety conjecture for quantum gravity with polynomial Riemann tensor interactions of the form $\sim\int \sqrt{g} \,(R_{\mu\nu\sigma\tau}R^{\mu\nu\sigma\tau})^n$ and $\sim\int \sqrt{g} \, R\cdot(R_{\mu\nu\sigma\tau}R^{\mu\nu\sigma\tau})^n$, and functions thereof.
• Interacting fixed points, universal scaling dimensions, gaps in eigenvalue spectra, quantum equations of motion, and de Sitter solutions are identified by combining high order polynomial approximations, Pad\'e resummations, and full numerical integration.