Fixed-Functionals of three-dimensional Quantum Einstein Gravity

We study the non-perturbative renormalization group flow of f(R)-gravity in three-dimensional Asymptotically Safe Quantum Einstein Gravity. Within the conformally reduced approximation, we derive an exact partial differential equation governing the RG-scale dependence of the function f(R). This equation is shown to possess two isolated and one continuous one-parameter family of scale-independent, regular solutions which constitute the natural generalization of RG fixed points to the realm of infinite-dimensional theory spaces. All solutions are bounded from below and give rise to positive definite kinetic terms. Moreover, they admit either one or two UV-relevant deformations, indicating that the corresponding UV-critical hypersurfaces remain finite dimensional despite the inclusion of an infinite number of coupling constants. The impact of our findings on the gravitational Asymptotic Safety program and its connection to new massive gravity is briefly discussed.Comment: 34 pages, 14 figure

RG flows of Quantum Einstein Gravity on maximally symmetric spaces

We use the Wetterich-equation to study the renormalization group flow of $f(R)$-gravity in a three-dimensional, conformally reduced setting. Building on the exact heat kernel for maximally symmetric spaces, we obtain a partial differential equation which captures the scale-dependence of $f(R)$ for positive and, for the first time, negative scalar curvature. The effects of different background topologies are studied in detail and it is shown that they affect the gravitational RG flow in a way that is not visible in finite-dimensional truncations. Thus, while featuring local background independence, the functional renormalization group equation is sensitive to the topological properties of the background. The detailed analytical and numerical analysis of the partial differential equation reveals two globally well-defined fixed functionals with at most a finite number of relevant deformations. Their properties are remarkably similar to two of the fixed points identified within the $R^2$-truncation of full Quantum Einstein Gravity. As a byproduct, we obtain a nice illustration of how the functional renormalization group realizes the "integrating out" of fluctuation modes on the three-sphere.Comment: 35 pages, 6 figure

Scheme dependence and universality in the functional renormalization group

We prove that the functional renormalization group flow equation admits a perturbative solution and show explicitly the scheme transformation that relates it to the standard schemes of perturbation theory. We then define a universal scheme within the functional renormalization group.Comment: 5 pages, improved version; v2: published version; v3 and v4: fixed various typos (final result is unaffected

RG flows of Quantum Einstein Gravity in the linear-geometric approximation

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 comes with similar properties as the one found in metric Quantum Einstein Gravity; in particular it possesses three UV-relevant directions and is stable with respect to deformations of the regulator functions by endomorphisms.Comment: 32 pages, 4 figue

Macromolecular dynamics in red blood cells investigated using neutron spectroscopy

We present neutron scattering measurements on the dynamics of hemoglobin (Hb) in human red blood cells in vivo. Global and internal Hb dynamics were measured in the ps to ns time- and {\AA} length-scale using quasielastic neutron backscattering spectroscopy. We observed the cross-over from global Hb short-time to long-time self-diffusion. Both short- and long-time diffusion coefficients agree quantitatively with predicted values from hydrodynamic theory of non-charged hard-sphere suspensions when a bound water fraction of around 0.23g H2O/ g Hb is taken into account. The higher amount of water in the cells facilitates internal protein fluctuations in the ps time-scale when compared to fully hydrated Hb powder. Slower internal dynamics of Hb in red blood cells in the ns time-range were found to be rather similar to results obtained with fully hydrated protein powders, solutions and E. coli cells