Impact of topology in foliated Quantum Einstein Gravity

Understand

We use a functional renormalization group equation tailored to the Arnowitt-Deser-Misner formulation of gravity to study the scale-dependence of Newton's coupling and the cosmological constant on a background spacetime with topology S^1xS^d.

• The resulting beta functions possess a non-trivial renormalization group fixed point, which may provide the high-energy completion of the theory through the asymptotic safety mechanism.
• The fixed point is robust with respect to changing the parametrization of the metric fluctuations and regulator scheme.
• The phase diagrams show that this fixed point is connected to a classical regime through a crossover.