Asymptotically safe gravity is one effective approach to quantum gravity. It is important to differentiate the modified gravity inspired by asymptotically safe gravity. In this paper, we examine the matter particles dynamics near the improved version of Schwarzschild black hole. We assume that in the context of asymptotically safe gravity scenario the ambient matter surrounding the black hole is of isothermal in nature and investigate the spherical accretion of matter by deriving solutions at critical points. The analysis for the various values of the state parameter for isothermal test fluids, viz., $k=1,~1/2,~1/3,~1/4$ show the possibility of accretion onto asymptotically safe black hole. We formulate the accretion problem as Hamiltonian dynamical system and explain its phase flow in detail which reveals interesting results in asymptotically safe gravity theory.
This is an introduction to asymptotically safe quantum gravity, explaining the main idea of asymptotic safety and how it could solve the problem of predictivity in quantum gravity. In the first part, the concept of an asymptotically safe fixed point is discussed within the functional Renormalization Group framework for gravity, which is also briefly reviewed. A concise overview of key results on asymptotically safe gravity is followed by a short discussion of important open questions. The second part highlights how the interplay with matter provides observational consistency tests for all quan…
We investigate the impact of quantum gravity on accretion onto a modified Schwarzschild black hole within the context of the generalized uncertainty principle (GUP). The minimal measurable length connected to GUP modifies the Schwarzschild black hole, giving it the capacity to accommodate the correction due to quantum gravity. We look at potential critical point locations and calculate the critical speed of the matter accreting. We determine the temperature and total integrated flux correction at the event horizon for the polytropic matter using the least measurable length conjecture offered b…
Matter-quantum gravity interactions can be used for direct and also indirect experimental tests of quantum gravity. We focus on photon-photon scattering in asymptotically safe gravity as a direct test of the small-scale structure of spacetime, and discuss how near-future experiments can probe asymptotic safety in a setting with large extra dimensions.
By studying the notion of a fundamentally minimal length scale in asymptotically safe gravity we find that a specific version of deformed special relativity (DSR) naturally arises in this approach. We then consider two thought experiments to examine the interpretation of the scenario and discuss similarities and differences to other approaches to DSR.
We comment on Weinberg's interesting analysis of asymptotically safe inflation (arXiv:0911.3165). We find that even if the gravity theory exhibits an ultraviolet fixed point, the energy scale during inflation is way too low to drive the theory close to the fixed point value. We choose the specific renormalization groupflow away from the fixed point towards the infrared region that reproduces the Newton's constant and today's cosmological constant. We follow this RG flow path to scales below the Planck scale to study the stability of the inflationary scenario. Again, we find that some fine tuni…
We explore the question why our universe is four dimensional from an asymptotically safe vantage point. We find hints that asymptotically safe quantum fluctuations of gravity can only solve the $U(1)$ Landau-pole problem in the Standard Model in four dimensions. This could single out the observed dimensionality of the universe as the critical dimensionality of asymptotically safe interactions.
Four-dimensional Quantum Einstein Gravity (QEG) is likely to be an asymptotically safe theory which is applicable at arbitrarily small distance scales. On sub-Planckian distances it predicts that spacetime is a fractal with an effective dimensionality of 2. The original argument leading to this result was based upon the anomalous dimension of Newton's constant. In the present paper we demonstrate that also the spectral dimension equals 2 microscopically, while it is equal to 4 on macroscopic scales. This result is an exact consequence of asymptotic safety and does not rely on any truncation. C…
We present a general framework to systematically study the derivative expansion of asymptotically safe quantum gravity. It is based on an exact decoupling and cancellation of different modes in the Landau limit, and implements a correct mode count as well as a regularisation based on geometrical considerations. It is applicable independent of the truncation order. To illustrate the power of the framework, we discuss the quartic order of the derivative expansion and its fixed point structure as well as physical implications.
Within asymptotically safe Quantum Einstein Gravity (QEG), the quantum 4-sphere is discussed as a specific example of a fractal spacetime manifold. The relation between the infrared cutoff built into the effective average action and the corresponding coarse graining scale is investigated. Analyzing the properties of the pertinent cutoff modes, the possibility that QEG generates a minimal length scale dynamically is explored. While there exists no minimal proper length, the QEG sphere appears to be "fuzzy" in the sense that there is a minimal angular separation below which two points cannot be …
To find out the possible scenarios for quantum gravity consistent with the observed universe, we numerically investigate the non-perturbative renormalization group equations of a general quadratic gravity theory recently derived by Sen, Wetterich and Yamada (\textit{JHEP} 03 (2022) 130). As boundary conditions, we impose consistency with the Hubble scale and the laboratory scale experiments, and the Starobinsky model of inflation. We find two kinds of trajectories which go to different regime at the trans-Planckian scales: i) a trajectory which flows to the asymptotically free regime, and ii) …
Asymptotically Safe theories of gravity have recently received much attention. In this work we discuss a class of inflationary models derived from quantum-gravity modification of quadratic gravity according to the induced scaling around the non-Gaussian fixed point at very high energies. It is argued that the presence of a three dimensional ultraviolet critical surface generates operators of non-integer power of the type $R^{2-θ/2}$ in the effective Lagrangian, where $θ>0$ is a critical exponent. The requirement of a successful inflationary model in agreement with the recent Planck 2015 data p…
In this paper we investigate the perturbation theory of the asymptotically safe inflation and we find that all modes of gravitational waves perturbation become ghosts in order to achieve a large enough number of e-folds. Formally we can calculate the power spectrum of gravitational waves perturbation, but we find that it is negative. It indicates that there is serious trouble with the asymptotically safe inflation.
Entanglement entropies calculated in the framework of quantum field theory on classical, flat or curved, spacetimes are known to show an intriguing area law in four dimensions, but they are also notorious for their quadratic ultraviolet divergences. In this paper we demonstrate that the analogous entanglement entropies when computed within the Asymptotic Safety approach to background independent quantum gravity are perfectly free from such divergences. We argue that the divergences are an artifact due to the over-idealization of a rigid, classical spacetime geometry which is insensitive to the…
We explore the fate of the curvature singularity of Schwarzschild (deSitter) black holes in asymptotically safe quantum gravity. Specifically, we upgrade the classical spacetime by including the running of the Newton coupling and cosmological constant. In this setting, the antiscreening character of the gravitational interaction can remove the singularity, yet a nonzero value of the cosmological constant in the ultraviolet appears to reintroduce it. We find hints that a finite value of the cosmological constant in the infrared is compatible with singularity resolution provided that the cosmolo…
We review aspects of the interplay of asymptotically safe gravity with matter, focusing on the potential predictive power of the quantum scale-symmetry underlying the asymptotically safe fixed point. We explain how an asymptotically safe fixed point for the Standard Model, induced by quantum-gravity fluctuations, might i) render the Standard Model ultraviolet complete and ii) allow us to calculate the values of some of the Standard-Model couplings. In particular, we highlight that such a fixed point might explain the mass-difference between the top and bottom quark.
We explore whether quantum gravity effects within the asymptotic safety paradigm can provide a predictive ultraviolet completion for Abelian gauge theories. We evaluate the effect of quantum gravity fluctuations on the running couplings in the gauge sector and discover an asymptotically safe fixed point of the Renormalization Group. In particular, if the strength of gravitational interactions remains below a critical strength, the minimal gauge coupling becomes asymptotically free. Further, we point out that a completely asymptotically free dynamics for the gauge field is impossible to achieve…
The gravitational asymptotic safety program strives for a consistent and predictive quantum theory of gravity based on a non-trivial ultraviolet fixed point of the renormalization group (RG) flow. We investigate this scenario by employing a novel functional renormalization group equation which takes the causal structure of space-time into account and connects the RG flows for Euclidean and Lorentzian signature by a Wick-rotation. Within the Einstein-Hilbert approximation, the $β$-functions of both signatures exhibit ultraviolet fixed points in agreement with asymptotic safety. Surprisingly, th…
The field of asymptotically safe matter-gravity systems is maturing from the study of simple toy models to the exploration of sectors of the Standard Model and beyond. This status update reviews the current state of the art and points out open questions and future perspectives.
We investigate axion-like particles (ALPs) in the context of asymptotically safe gravity-matter systems. The ALP-photon interaction, which facilitates experimental searches for ALPs, is a dimension-5-operator. Quantum fluctuations of gravity lower its scaling dimension, and the ALP-photon coupling can become asymptotically free or even asymptotically safe. However, quantum fluctuations of gravity need to be strong to overcome the canonical scaling and this strong-gravity regime is in tension with the weak-gravity bound in asymptotic safety. Thus, we tentatively conclude that fundamental ALPs c…
Within the Asymptotic Safety scenario, we discuss whether Quantum Einstein Gravity (QEG) can give rise to a semi-classical regime of propagating physical gravitons (gravitational waves) governed by an effective theory which complies with the standard rules of local quantum field theory. According to earlier investigations based on single-metric truncations there is a tension between this requirement and the condition of Asymptotic Safety since the former (latter) requires a positive (negative) anomalous dimension of Newton's constant. We show that the problem disappears using the bi-metric ren…
Asymptotic safety generalizes asymptotic freedom and could contribute to understanding physics beyond the Standard Model. It is a candidate scenario to provide an ultraviolet extension for the effective quantum field theory of gravity through an interacting fixed point of the Renormalization Group. Recently, asymptotic safety has been established in specific gauge-Yukawa models in four dimensions in perturbation theory, providing a starting point for asymptotically safe model building. Moreover, an asymptotically safe fixed point might even be induced in the Standard Model under the impact of …
We use functional renormalization group methods to study gravity minimally coupled to a free scalar field. This setup provides the prototype of a gravitational theory which is perturbatively non-renormalizable at one-loop level, but may possess a non-trivial renormalization group fixed point controlling its UV behavior. We show that such a fixed point indeed exists within the truncations considered, lending strong support to the conjectured asymptotic safety of the theory. In particular, we demonstrate that the counterterms responsible for its perturbative non-renormalizability have no qualita…
We summarize the status of constructing fixed functionals within the f(R)-truncation of Quantum Einstein Gravity in three spacetime dimensions. Focusing on curvatures much larger than the IR-cutoff scale, it is shown that the fixed point equation admits three different scaling regimes: for classical and quantum dominance the equation becomes linear and has power-law solutions, while the balanced case gives rise to a generalized homogeneous equation whose order is reduced by one and whose solutions are non-analytical.
Asymptotic safety is a theoretical proposal for the ultraviolet completion of quantum field theories, in particular for quantum gravity. Significant progress on this program has led to a first characterization of the Reuter fixed point. Further advancement in our understanding of the nature of quantum spacetime requires addressing a number of open questions and challenges. Here, we aim at providing a critical reflection on the state of the art in the asymptotic safety program, specifying and elaborating on open questions of both technical and conceptual nature. We also point out systematic pat…
Inflation is studied in the context of asymptotically safe theories of gravitation. Conditions are explored under which it is possible to have a long period of nearly exponential expansion that eventually comes to an end.
4D Einstein gravity coupled to scalars and abelian gauge fields in its 2-Killing vector reduction is shown to be quasi-renormalizable to all loop orders at the expense of introducing infinitely many essential couplings. The latter can be combined into one or two functions of the `area radius' associated with the two Killing vectors. The renormalization flow of these couplings is governed by beta functionals expressible in closed form in terms of the (one coupling) beta function of a symmetric space sigma-model. Generically the matter coupled systems are asymptotically safe, that is the flow po…
We compute the ghost anomalous dimension within the asymptotic-safety scenario for quantum gravity. For a class of covariant gauge fixings and using a functional RG scheme, the anomalous dimension $η_c$ is negative, implying an improved UV behavior of ghost fluctuations. At the non-Gaussian UV fixed point, we observe a maximum value of $η_c\simeq -0.78$ for the Landau-deWitt gauge within the given scheme and truncation. Most importantly, the backreaction of the ghost flow onto the Einstein-Hilbert sector preserves the non-Gaussian fixed point with only mild modifications of the fixed-point val…
We discuss the existence of inflationary solutions in a class of renormalization group improved polynomial f(R) theories, which have been studied recently in the context of the asymptotic safety scenario for quantum gravity. These theories seem to possess a nontrivial ultraviolet fixed point, where the dimensionful couplings scale according to their canonical dimensionality. Assuming that the cutoff is proportional to the Hubble parameter, we obtain modified Friedmann equations which admit both power law and exponential solutions. We establish that for sufficiently high order polynomial the so…
Asymptotically safe theories of gravitation have received great attention in recent times. In this framework an effective action embodying the basic features of the renormalized flow around the non-gaussian fixed point is derived and its implications for the early universe are discussed. In particular, a "landscape" of a countably infinite number of cosmological inflationary solutions characterized by an unstable de Sitter phase lasting for a large enough number of e-folds is found.
The weak-gravity bound has been discovered in asymptotically safe gravity-matter systems, where it limits the maximum strength of gravitational fluctuations. In the present paper, we explore it for the first time in systems with more than one gauge field, to discover whether systems with 12 gauge fields (like the Standard Model) exhibit a weak-gravity bound and whether the gravitational fixed point evades it. Further, we test the robustness of the present and previous results on the weak-gravity bound by exploring their dependence on a gravitational gauge parameter. Finally, the existence of t…
In this paper we study the traversability of a wormhole in the context of Asymptotically Safe Gravity (ASG) for two different cases, namely, the spherical case and the pseudospherical case. We carried out an analysis in the throat of the wormhole with an specific choice of the cutoff function $f=ξR$. Recently, this study has been performed in Ref \cite{Moti:2020whf}, however the authors consider only a classical source with constant state parameter $ω$. Here we have generalized their study in two ways: a) with a classical state parameter which is dependent of the position $ω(r)$ and b) with an…
Asymptotically safe quantum gravity is a promising candidate scenario to provide a UV extension for the effective quantum field theory of Einstein's gravity. The theory has its foundations on the very successful framework of quantum field theory, which has been extensively tested for electromagnetic and nuclear interactions. However, observational tests of asymptotically safe quantum gravity are more challenging. Recently, a rotating black hole metric inspired by asymptotically safe quantum gravity has been proposed, and this opens the possibility of astrophysical tests of the theory. In the p…
Niels Bohr Institute（尼尔斯·玻尔研究所）；Niels Bohr International Academy（尼尔斯·玻尔国际学院）；SISSA - International School for Advanced Studies（SISSA-高级研究国际学院）；INFN, Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；IFPU - Institute for Fundamental Physics of the Universe（宇宙基础物理研究所）
In this paper we study a class of wormhole solutions called generalized Ellis-Bronnikov wormholes in the context of asymptotically safe gravity (ASG). These solutions are characterized by two parameters: an even number $n$ and the wormhole throat radius $r_t$. The particular case $n=2$ recovers the usual Ellis-Bronnikov spacetime, which has already been addressed in the literature. We analyzed the nature of matter in the wormhole's throat, and in nearby regions, of these generalized solutions with $n>2$, using three curvature scalars in the ASG approach, namely, the Ricci scalar, squared Ricci…
We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck-scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works \cite{Christiansen:2015rva, Meibohm:2015twa}, concludes that gravity-induced chiral symmetry breaking at the Planck s…
Motivated by conformal field theory studies we investigate Quantum Einstein Gravity with a new field parametrization where the dynamical metric is basically given by the exponential of a matrix-valued fluctuating field, $g_{μν}=\bar{g}_{μρ}(e^h)^ρ_ν$. In this way, we aim to reproduce the critical value of the central charge when considering $2+ε$ dimensional spacetimes. With regard to the Asymptotic Safety program, we take special care of possible fixed points and new structures of the corresponding RG flow in $d=4$ for both single- and bi-metric truncations. Finally, we discuss the issue of r…
We compute the effective potential for scalar fields in asymptotically safe quantum gravity. A scaling potential and other scaling functions generalize the fixed point values of renormalizable couplings. The scaling potential takes a non-polynomial form, approaching typically a constant for large values of scalar fields. Spontaneous symmetry breaking may be induced by non-vanishing gauge couplings. We strengthen the arguments for a prediction of the ratio between the masses of the top quark and the Higgs boson. Higgs inflation in the standard model is unlikely to be compatible with asymptotic …
We study the quantum modifications of classical, spherically symmetric Schwarzschild (Anti-) de Sitter black holes within Quantum Einstein Gravity. The quantum effects are incorporated through the running coupling constants $G_k$ and $Λ_k$, computed within the exact renormalization group approach, and a common scale-setting procedure. We find that, in contrast to common intuition, it is actually the cosmological constant that determines the short-distance structure of the RG-improved black hole: in the asymptotic UV the structure of the quantum solutions is universal and given by the classical…
We study the fixed point structure of the Higgs-Yukawa model, with its scalar being non-minimally coupled to the asymptotically safe gravity, using the functional renormalization group. We have obtained the renormalization group equations for the cosmological and Newton constants, the scalar mass-squared and quartic coupling constant, and the Yukawa and non-minimal coupling constants, taking into account all the scalar, fermion, and graviton loops. We find that switching on the fermionic quantum fluctuations makes the non-minimal coupling constant irrelevant around the Gaussian-matter fixed po…
Asymptotic Safety implies that observables including scattering amplitudes remain finite at the highest energy scales. Traditionally, this feature is connected to an interacting fixed point of the Wilsonian renormalization group that provides the high-energy completion of the theory. In this article, we discuss a different facet of Asymptotic Safety, reviewing its imprint on the quantum effective action. We start with a concise introduction to the form factor framework for gravity and gravity-matter systems, before giving an encyclopaedic overview of gravity-mediated scattering amplitudes deri…
The asymptotic safety program strives for a consistent description of gravity as a non-perturbatively renormalizable quantum field theory. In this framework the gravitational interactions are encoded in a renormalization group flow connecting the quantum gravity regime at trans-Planckian scales to observable low-energy physics. Our proceedings reviews the key elements underlying the predictive power of the construction and summarizes the state-of-the-art in determining its free parameters. The explicit construction of a realistic renormalization group trajectory describing our world shows that…
Investigations of Quantum Einstein Gravity (QEG) based upon the effective average action employ a flow equation which does not contain any ultraviolet (UV) regulator. Its renormalization group trajectories emanating from a non-Gaussian fixed point define asymptotically safe quantum field theories. A priori these theories are, somewhat unusually, given in terms of their effective rather than bare action. In this paper we construct a functional integral representation of these theories. We fix a regularized measure and show that every trajectory of effective average actions, depending on an IR c…
The gauge hierarchy problem could find a solution within the scenario of asymptotic safety for quantum gravity. We discuss a "resurgence mechanism" where the running dimensionless coupling responsible for the Higgs scalar mass first decreases in the ultraviolet regime and subsequently increases in the infrared regime. A gravity induced large anomalous dimension plays a crucial role for the required "self-tuned criticality" in the ultraviolet regime beyond the Planck scale.
The asymptotic safety scenario in gravity is accessed within the systematic vertex expansion scheme for functional renormalisation group flows put forward in \cite{Christiansen:2012rx,Christiansen:2014raa}, and implemented in \cite{Christiansen:2015rva} for propagators and three-point functions. In the present work this expansion scheme is extended to the dynamical graviton four-point function. For the first time, this provides us with a closed flow equation for the graviton propagator: all vertices and propagators involved are computed from their own flows. In terms of a covariant operator ex…
A recently proposed Asymptotically Safe cosmology provides an elegant mechanism towards understanding the nature of dark energy and its associated cosmic coincidence problem. The underlying idea is that the accelerated expansion of the universe can occur due to infrared quantum gravity modifications at intermediate astrophysical scales (galaxies or galaxy clusters) which produce local anti-gravity sources. In this cosmological model no extra unproven energy scales or fine-tuning are used. In this study the Asymptotically Safe model is confronted with the most recent observational data from low…
The asymptotic safety scenario of gravity conjectures that (i) the quantum field theory of gravity exists thanks to the presence of a non-trivial ultraviolet fixed point of the renormalization group, and that (ii) the fixed point has only a finite number of relevant perturbations, i.e. a finite number of UV-stable directions (or in other words, a finite number of free parameters to be fixed experimentally). Within the f(R) approximation of the functional renormalization group equation of gravity, we show that assuming the first half of the conjecture to be true, the remaining half follows from…
Black holes are among the most fascinating objects populating our universe. Their characteristic features, encompassing spacetime singularities, event horizons, and black hole thermodynamics, provide a rich testing ground for quantum gravity ideas. In this note we observe that the renormalization group improved Schwarzschild black holes constructed by Bonanno and Reuter within Weinberg's asymptotic safety program constitute a prototypical example of a Hayward geometry used to model non-singular black holes within quantum gravity phenomenology. Moreover, they share many features of a Planck sta…
We construct a new inflation model in which the standard model Higgs boson couples minimally to gravity and acts as the inflaton. Our construction of Higgs inflation incorporates the standard model with Einstein gravity which exhibits asymptotic safety in the ultraviolet region. The slow roll condition is satisfied at large field value due to the asymptotically safe behavior of Higgs self-coupling at high energies. We find that this minimal construction is highly predictive, and is consistent with both cosmological observations and collider experiments.
We use the non-Gaussian fixed points (NGFPs) appearing in the renormalization group flow of gravity and gravity-matter systems to construct models of NGFP-driven inflation via a renormalization group improvement scheme. The cosmological predictions of these models depend sensitively on the characteristic properties of the NGFPs, including their position and stability coefficients, which in turn are determined by the field content of the underlying matter sector. We demonstrate that the NGFPs appearing in gravity-matter systems where the matter content is close to the one of the standard model …
According to the asymptotic safety conjecture, gravity is a renormalizable quantum field theory whose continuum limit is defined by an interacting fixed point of the renormalization group flow. In these proceedings we review some implications of the existence of this non-trivial fixed point in cosmological contexts. Specifically, we discuss a toy model exemplifying how the departure from the fixed-point regime can explain the approximate scale-invariance of the power spectrum of temperature fluctuations in the cosmic microwave background.
