Asymptotically safe f(R)-gravity coupled to matter I: the polynomial case

We use the functional renormalization group equation for the effective average action to study the non-Gaussian renormalization group fixed points (NGFPs) arising within the framework of f(R)-gravity minimally coupled to an arbitrary number of scalar, Dirac, and vector fields. Based on this setting we provide comprehensible estimates which gravity-matter systems give rise to NGFPs suitable for rendering the theory asymptotically safe. The analysis employs an exponential split of the metric fluctuations and retains a 7-parameter family of coarse-graining operators allowing the inclusion of non-trivial endomorphisms in the regularization procedure. For vanishing endomorphisms, it is established that gravity coupled to the matter content of the standard model of particle physics and many beyond the standard model extensions exhibit NGFPs whose properties are strikingly similar to the case of pure gravity: there are two UV-relevant directions and the position and critical exponents converge rapidly when higher powers of the scalar curvature are included. Conversely, none of the phenomenologically interesting gravity-matter systems exhibits a stable NGFP when a Type II coarse graining operator is employed. Our analysis resolves this tension by demonstrating that the NGFPs seen in the two settings belong to different universality classes.Comment: 49 pages, 5 figure

Effective Supergravity Actions for Conifold Transitions

We construct gauged supergravity actions which describe the dynamics of M-theory on a Calabi-Yau threefold in the vicinity of a conifold transition. The actions explicitly include N charged hypermultiplets descending from wrapped M2-branes which become massless at the conifold point. While the vector multiplet sector can be treated exactly, we approximate the hypermultiplet sector by the non-compact Wolf spaces X(1+N). The effective action is then uniquely determined by the charges of the wrapped M2-branes.Comment: 57 pages, no figure

Towards reconstructing the quantum effective action of gravity

Starting from a parameterisation of the quantum effective action for gravity we calculate correlation functions for observable quantities. The resulting templates allow to reverse-engineer the couplings describing the effective dynamics from the correlation functions. Applying this new formalism to the autocorrelation function of spatial volume fluctuations measured within the Causal Dynamical Triangulations program suggests that the corresponding quantum effective action consists of the Einstein-Hilbert action supplemented by a non-local interaction term. We expect that our matching-template formalism can be adapted to a wide range of quantum gravity programs allowing to bridge the gap between the fundamental formulation and observable low-energy physics.Comment: 6 pages, 1 figure; v2: reference update+clarification; v3: matches published versio

Asymptotically safe cosmology - a status report

Asymptotic Safety, based on a non-Gaussian fixed point of the gravitational renormalization group flow, provides an elegant mechanism for completing the gravitational force at sub-Planckian scales. At high energies the fixed point controls the scaling of couplings such that unphysical divergences are absent while the emergence of classical low-energy physics is linked to a crossover between two renormalization group fixed points. These features make Asymptotic Safety an attractive framework for cosmological model building. The resulting scenarios may naturally give rise to a quantum gravity driven inflationary phase in the very early universe and an almost scale-free fluctuation spectrum. Moreover, effective descriptions arising from an renormalization group improvement permit a direct comparison to cosmological observations as, e.g. Planck data.Comment: Invited review for the special issue "Testing quantum gravity with cosmology" to appear in Compte Rendus Physique

Functional Renormalization Group flows on Friedman-Lema\^{\i}tre-Robertson-Walker backgrounds

We reanalyze the construction of the gravitational functional renormalization group equation tailored to the Arnowitt-Deser-Misner formulation emphasizing its connection to the covariant formulation. The results obtained from projecting the renormalization group flow onto the Einstein-Hilbert action are reviewed in detail and we provide a novel example illustrating how the formalism may be connected to the Causal Dynamical Triangulations approach to quantum gravity.Comment: 14 pages, 2 figure