0000000000304165
AUTHOR
Maximilian Demmel
showing 2 related works from this author
Connections and geodesics in the space of metrics
2015
We argue that the exponential relation $g_{\mu\nu} = \bar{g}_{\mu\rho}\big(\mathrm{e}^h\big)^\rho{}_\nu$ is the most natural metric parametrization since it describes geodesics that follow from the basic structure of the space of metrics. The corresponding connection is derived, and its relation to the Levi-Civita connection and the Vilkovisky-DeWitt connection is discussed. We address the impact of this geometric formalism on quantum gravity applications. In particular, the exponential parametrization is appropriate for constructing covariant quantities like a reparametrization invariant effective action in a straightforward way. Furthermore, we reveal an important difference between Eucli…
RG flows of Quantum Einstein Gravity in the linear-geometric approximation
2014
We construct a novel Wetterich-type functional renormalization group equation for gravity which encodes the gravitational degrees of freedom in terms of gauge-invariant fluctuation fields. Applying a linear-geometric approximation the structure of the new flow equation is considerably simpler than the standard Quantum Einstein Gravity construction since only transverse-traceless and trace part of the metric fluctuations propagate in loops. The geometric flow reproduces the phase-diagram of the Einstein-Hilbert truncation including the non-Gaussian fixed point essential for Asymptotic Safety. Extending the analysis to the polynomial $f(R)$-approximation establishes that this fixed point come…