Article (Published Version) http://sro.sussex.ac.uk Falls, K, Litim, D, Nikolakopoulos, K and Rahmede, C (2016) Further evidence for asymptotic safety of quantum gravity. Physical Review D, 93 (10). p. 104022. ISSN 1550-7998 This version is available from Sussex Research Online: http://sro.sussex.ac.uk/63626/ This document is made available in accordance with publisher policies and may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the URL above for details on accessing the published version. Copyright and reuse:Sussex Research Online is a digital repository of the research output of the University.Copyright and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable, the material made available in SRO has been checked for eligibility before being made available.Copies of full text items generally can be reproduced, displayed or performed and given to third parties in any format or medium for personal research or study, educational, or not-for-profit purposes without prior permission or charge, provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way.Further evidence for asymptotic safety of quantum gravity The asymptotic safety conjecture is examined for quantum gravity in four dimensions. Using the renormalization group, we find evidence for an interacting UV fixed point for polynomial actions up to the 34th power in the Ricci scalar. The extrapolation to infinite polynomial order is given, and the selfconsistency of the fixed point is established using a bootstrap test. All details of our analysis are provided. We also clarify further aspects such as stability, convergence, the role of boundary conditions, and a partial degeneracy of eigenvalues. Within this setting we find strong support for the conjecture.

We investigate the asymptotic safety conjecture for quantum gravity including curvature invariants beyond Ricci scalars. Our strategy is put to work for families of gravitational actions which depend on functions of the Ricci scalar, the Ricci tensor, and products thereof. Combining functional renormalization with high order polynomial approximations and full numerical integration we derive the renormalization group flow for all couplings and analyse their fixed points, scaling exponents, and the fixed point effective action as a function of the background Ricci curvature. The theory is characterized by three relevant couplings. Higher-dimensional couplings show near-Gaussian scaling with increasing canonical mass dimension. We find that Ricci tensor invariants stabilize the UV fixed point and lead to a rapid convergence of polynomial approximations. We apply our results to models for cosmology and establish that the gravitational fixed point admits inflationary solutions. We also compare findings with those from fðRÞ-type theories in the same approximation and pin-point the key new effects due to Ricci tensor interactions. Implications for the asymptotic safety conjecture of gravity are indicated.

Quantum gravitational corrections to black holes are studied in four and higher dimensions using a renormalisation group improvement of the metric. The quantum effects are worked out in detail for asymptotically safe gravity, where the short-distance physics is characterized by a nontrivial fixed point of the gravitational coupling. We find that a weakening of gravity implies a decrease of the event horizon, and the existence of a Planck-size black hole remnant with vanishing temperature and vanishing heat capacity. The absence of curvature singularities is generic and discussed together with the conformal structure and the Penrose diagram of asymptotically safe black holes. The production cross-section of mini-black holes in energetic particle collisions, such as those at the Large Hadron Collider, is analysed within low-scale quantum gravity models. Quantum gravity corrections imply that cross-sections display a threshold, are suppressed in the Planckian, and reproduce the semiclassical result in the deep trans-Planckian region. Further implications are discussed.

We study fixed points of quantum gravity with renormalisation group methods, and a procedure to remove convergence-limiting poles from the flow. The setup is tested within the f (R) approximation for gravity by solving exact recursive relations up to order R 70 in the Ricci scalar, combined with resummations and numerical integration. Results include fixed points, scaling exponents, gap in the eigenvalue spectrum, dimensionality of the UV critical surface, fingerprints for weak coupling, and quantum equations of motion. Our findings strengthen the view that "most of quantum gravity" is rather weakly coupled. Another novelty are a pair of de Sitter solutions for quantum cosmology, whose occurrence is traced back to the removal of poles. We also address slight disparities of results in the literature, and give bounds on the number of fundamentally free parameters of quantum gravity.

We investigate the phase diagram of quantum gravity with a vertex expansion about constantlycurved backgrounds. The graviton two-and three-point function are evaluated with a spectral sum on a sphere. We obtain, for the first time, curvature-dependent UV fixed point functions of the dynamical fluctuation couplings g * (R), µ * (R), and λ * 3 (R), and the background f (R)-potential. Based on these fixed point functions we compute solutions to the quantum and the background equation of motion with and without Standard Model matter. We have checked that the solutions are robust against changes of the truncation.