The structure of the divergences for transverse theories of gravity is studied to one-loop order. These theories are invariant only under those diffeomorphisms that enjoy unit Jacobian determinant (TDiff), so that the determinant of the metric transforms as a true scalar instead of a density. Generically, the models include an additional scalar degree of freedom contained in the metric besides the usual spin two component. When the cosmological constant is fine tuned to zero, there are only two theories which are on shell finite, namely the one in which the symmetry is enhanced to the full group of diffeomorphisms, i.e. Einstein's gravity, and another one denoted by WTDiff which enjoys local Weyl invariance. Both of them are free from the additional scalar.
This work presents a study of the possibility for extending the well-known results of E.Verlinde concerning the entropic nature of gravity to the ultraviolet region (Planck's energies) and also the derivation of quantum corrections to Einstein Equations
We discuss the existence and properties of a nontrivial fixed point in f(R)-gravity, where f is a polynomial of order up to six. Within this seven-parameter class of theories, the fixed point has three ultraviolet-attractive and four ultraviolet-repulsive directions; this brings further support to the hypothesis that gravity is nonperturbatively renormalizabile.
An ultraviolet complete quantum gravity theory is formulated in which vertex functions in Feynman graphs are entire functions and the propagating graviton is described by a local, causal propagator. The cosmological constant problem is investigated in the context of the ultraviolet complete quantum gravity.
The non-trivial ultraviolet fixed point in quantum gravity is calculated by means of the exact renormalization group equation in d-dimensions $(2\simeq d\leq4)$. It is shown that the ultraviolet non-Gaussian fixed point which is expected from the perturbatively $ε$-expanded calculations in $2+ε$ gravity theory remains in d=4. Hence it is possible that quantum gravity is an asymptotically safe theory and renormalizable in 2<d.
We study the Faddeev-Popov ghost sector of asymptotically safe quantum gravity, which becomes non-perturbative in the ultraviolet. We point out that nonzero matter-ghost couplings and higher-order ghost self-interactions exist at a non-Gaussian fixed point for the gravitational couplings, i.e., in the ultraviolet. Thus the ghost sector in this non-perturbative ultraviolet completion does not keep the structure of a simple Faddeev-Popov determinant. We discuss implications of the new ghost couplings for the Renormalization Group flow in gravity, the form of the ultraviolet completion, and the r…
Horava gravity is a proposal for completing general relativity in the ultraviolet by interactions that violate Lorentz invariance at very high energies. We focus on (2+1)-dimensional projectable Horava gravity, a theory which is renormalizable and perturbatively ultraviolet-complete, enjoying an asymptotically free ultraviolet fixed point. Adding a small cosmological constant to regulate the long distance behavior of the metric, we search for all circularly symmetric stationary vacuum solutions with vanishing angular momentum and approaching the de Sitter metric with a possible angle deficit a…
We study the ultraviolet stability of gravity-matter systems for general numbers of minimally coupled scalars and fermions. This is done within the functional renormalisation group setup put forward in \cite{Christiansen:2015rva} for pure gravity. It includes full dynamical propagators and a genuine dynamical Newton's coupling, which is extracted from the graviton three-point function. We find ultraviolet stability of general gravity-fermion systems. Gravity-scalar systems are also found to be ultraviolet stable within validity bounds for the chosen generic class of regulators, based on the si…
We study the beta functions for four-dimensional conformal gravity using two different parametrizations of metric fluctuation, linear split and exponential parametrization. We find that after imposing the traceless conditions, the beta functions are the same in four dimensions though the dependence on the dimensions are quite different. This indicates the universality of these results. We also examine the beta functions in general quadratic theory with the Einstein and cosmological terms for exponential parametrization, and find that it leads to results for beta functions of dimensionful coupl…
A local phenomenological model that reduces to a non-local gravitational theory giving dark energy is proposed. The non-local gravity action is known to fit the data as well as $Λ$-CDM thereby demanding a more fundamental local treatment. It is seen that the scale-invariant higher-derivative scalar-tensor theory of gravity, which is known to be ultraviolet perturbative renormalizable to all loops and where ghosts become innocuous, generates non-locality at low energies. The local action comprises of two real scalar fields coupled non-minimally with the higher-derivative gravity action. When on…
Indefinite causal structure is generically present in theories of quantum gravity admitting a path integral formulation. We show that summing over causal structures eliminates ultraviolet divergences of matter QFT and resolves spacetime singularities using the non-perturbative World Quantum Gravity approach. Independent information-theoretic and model-independent considerations suggest that the mechanism of ultraviolet regularization by indefinite causal structure also applies to other theories of quantum gravity.
In this Letter we derive the gravity field equations by varying the action for an ultraviolet complete quantum gravity. Then we consider the case of a static source term and we determine an exact black hole solution. As a result we find a regular spacetime geometry: in place of the conventional curvature singularity extreme energy fluctuations of the gravitational field at small length scales provide an effective cosmological constant in a region locally described in terms of a de Sitter space. We show that the new metric coincides with the noncommutative geometry inspired Schwarzschild black …
In this contribution, we discuss the asymptotic safety scenario for quantum gravity with a functional renormalisation group approach that disentangles dynamical metric fluctuations from the background metric. We review the state of the art in pure gravity and general gravity-matter systems. This includes the discussion of results on the existence and properties of the asymptotically safe ultraviolet fixed point, full ultraviolet-infrared trajectories with classical gravity in the infrared, and the curvature dependence of couplings also in gravity-matter systems. The results in gravity-matter s…
We highlight how the existence of an ultraviolet completion for interacting Standard-Model type matter puts constraints on the viable microscopic dynamics of asymptotically safe quantum gravity within truncated Renormalization Group flows. A first constraint -- the weak-gravity bound -- is rooted in the destruction of quantum scale-invariance in the matter system by strong quantum-gravity fluctuations. A second constraint arises by linking Planck-scale dynamics to the dynamics at the electroweak scale. Specifically, we delineate how to extract a prediction of the top quark mass from asymptotic…
We clarify a point concerning the ultraviolet behaviour of the Quantum Field Theory of gravity, under the assumption of the existence of an ultraviolet Fixed Point. We explain why Newton's constant should to scale like the inverse of the square of the cutoff, even though it is technically inessential. As a consequence of this behaviour, the existence of an UV Fixed Point would seem to imply that gravity has a built-in UV cutoff when described in Planck units, but not necessarily in other units.
This letter constructs, making use of the on-shell spinor-helicity formalism, a possible ultraviolet completion of gravity following a "bottom-up" approach. The assumptions of locality, unitarity and causality i) require an infinite tower of resonances with increasing spin and quantized mass, ii) introduce a duality relation among crossed scattering channels, and iii) dress all gravitational amplitudes in the Standard Model with a form factor that closely resembles either the Veneziano or the Virasoro-Shapiro amplitude in string theory. As a consequence of unitarity, the theory predicts leadin…
We study renormalization group equations of quantum gravity in four dimensions. We find an ultraviolet fixed point in accordance with the asymptotic safety conjecture, and infrared fixed points corresponding to general relativity with positive, vanishing or negative cosmological constant. In a minisuperspace approximation, we additionally find a renormalization group limit cycle shielding the ultraviolet from the infrared fixed points. We discuss implications of this pattern for asymptotically safe gravity in the continuum and on the lattice.
We construct a Weyl transverse diffeomorphism invariant theory of symmetric teleparallel gravity by employing the Weyl compensator formalism. The low-energy dynamics has a single spin two gravition without a scalar degree of freedom. By construction, it is equivalent to the unimodular gravity (as well as the Einstein gravity) at the non-linear level.
In this paper we study the geometry and the thermodynamics of a holographic screen in the framework of the ultraviolet self-complete quantum gravity. To achieve this goal we construct a new static, neutral, non-rotating black hole metric, whose outer (event) horizon coincides with the surface of the screen. The space-time admits an extremal configuration corresponding to the minimal holographic screen and having both mass and radius equalling the Planck units. We identify this object as the space-time fundamental building block, whose interior is physically unaccessible and cannot be probed ev…
A new exact renormalization group equation for the effective average action of Euclidean quantum gravity is constructed. It is formulated in terms of the component fields appearing in the transverse-traceless decomposition of the metric. It facilitates both the construction of an appropriate infrared cutoff and the projection of the renormalization group flow onto a large class of truncated parameter spaces. The Einstein-Hilbert truncation is investigated in detail and the fixed point structure of the resulting flow is analyzed. Both a Gaussian and a non-Gaussian fixed point are found. If the …
I review the field-theoretic renomalization group approach to quantum gravity, built around the existence of a non-trivial ultraviolet fixed point in four dimensions. I discuss the implications of such a fixed point, found in three largely unrelated non-perturbative approaches, and how it relates to the vacuum state of quantum gravity, and specifically to the running of $G$. One distinctive feature of the new fixed point is the emergence of a second genuinely non-perturbative scale, analogous to the scaling violation parameter in non-abelian gauge theories. I argue that it is natural to identi…
We formulate a renormalizable quantum gravity in $2+ε$ dimensions by generalizing the nonlinear sigma model approach to string theory. We find that the theory possesses the ultraviolet stable fixed point if the central charge of the matter sector is in the range $0~<~c~<~25$. This may imply the existence of consistent quantum gravity theory in 3 and 4 dimensions. We compute the scaling dimensions of the relevant operators in the theory at the ultraviolet fixed point. We obtain a scaling relation between the cosmological constant and the gravitational constant, which is crucial for searching fo…
We study the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmology in the Weyl-transverse (WTDiff) gravity in a general space-time dimension. The WTDiff gravity is invariant under both the local Weyl (conformal) transformation and the volume preserving diffeormorphisms (transverse diffeomorphisms) and is believed to be equivalent to general relativity at least at the classical level (perhaps, even in the quantum regime). It is explicitly shown by solving the equations of motion that the FLRW metric is a classical solution in the WTDiff gravity only when the spatial metric is flat, that is, the …
We study classical solutions in the Weyl-transverse (WTDiff) gravity coupled to an electro-magnetic field in four space-time dimensions. The WTDiff gravity is invariant under both the local Weyl (conformal) transformation and the volume preserving diffeormorphisms (transverse diffeomorphisms) and is known to be equivalent to general relativity at least at the classical level (perhaps even in the quantum regime). In particular, we find that only in four space-time dimensions, the charged Reissner-Nordstrom black hole metric is a classical solution when it is expressed in the Cartesian coordinat…
We study four-dimensional quantum gravity using non-perturbative renormalization group methods. We solve the corresponding equations for the fully momentum-dependent propagator, Newton's coupling and the cosmological constant. For the first time, we obtain a global phase diagram where the non-Gaussian ultraviolet fixed point of asymptotic safety is connected via smooth trajectories to a classical infrared fixed point. The theory is therefore ultraviolet complete and deforms smoothly into classical gravity as the infrared limit is approached.
For any fundamental quantum field theory, unitarity, renormalizability, and relativistic invariance are considered to be essential properties. Unitarity is inevitably connected to the probabilistic interpretation of the quantum theory, while renormalizability guarantees its completeness. Relativistic invariance, in turn, is a symmetry which derives from the structure of spacetime. So far, the perturbative attempt to formulate a fundamental local quantum field theory of gravity based on the metric field seems to be in conflict with at least one of these properties. In quantum Hořava gravity, a …
I review the lattice approach to quantum gravity, and how it relates to the non-trivial ultraviolet fixed point scenario of the continuum theory. After a brief introduction covering the general problem of ultraviolet divergences in gravity and other non-renormalizable theories, I cover the general methods and goals of the lattice approach. An underlying theme is the attempt at establishing connections between the continuum renormalization group results, which are mainly based on diagrammatic perturbation theory, and the recent lattice results, which apply to the strong gravity regime and are i…
We consider a local phenomenological model to explain a non-local gravity scenario which has been proposed to address dark energy issues. This non-local gravity action has been seen to fit the data as well as $Λ$-CDM and therefore demands a more fundamental local treatment. The induced gravity model coupled with higher-derivative gravity is exploited for this proposal, as this perturbatively renormalizable model has a well-defined ultraviolet (UV) description where ghosts are evaded. We consider a generalised version of this model where we consider two coupled scalar fields and their non-minim…
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…
Evanescent operators such as the Gauss-Bonnet term have vanishing perturbative matrix elements in exactly D=4 dimensions. Similarly, evanescent fields do not propagate in D=4; a three-form field is in this class, since it is dual to a cosmological-constant contribution. In this Letter, we show that evanescent operators and fields modify the leading ultraviolet divergence in pure gravity. To analyze the divergence, we compute the two-loop identical-helicity four-graviton amplitude and determine the coefficient of the associated (non-evanescent) R^3 counterterm studied long ago by Goroff and Sag…
A theory of quantum gravity has been recently proposed by means of a novel quantization prescription, which is able to turn the poles of the free propagators that are due to the higher derivatives into fakeons. The classical Lagrangian contains the cosmological term, the Hilbert term, $\sqrt{-g}R_{μν}R^{μν}$ and $\sqrt{-g}R^{2}$. In this paper, we compute the one-loop renormalization of the theory and the absorptive part of the graviton self energy. The results illustrate the mechanism that makes renormalizability compatible with unitarity. The fakeons disentangle the real part of the self ene…
Theories of gravity invariant under those diffeomorphisms generated by transverse vectors, $\pd_\mξ^\m=0$ are considered. Such theories are dubbed transverse, and differ from General Relativity in that the determinant of the metric, $g$, is a transverse scalar. We comment on diverse ways in which these models can be constrained using a variety of observations. Generically, an additional scalar degree of freedom mediates the interaction, so the usual constraints on scalar-tensor theories have to be imposed. If the purely gravitational part is Einstein--Hilbert but the matter action is transvers…
We study the Gauss-Bonnet (GB) term as the leading higher-curvature correction to pure Einstein gravity. Assuming a tree-level ultraviolet completion free of ghosts or tachyons, we prove that the GB term has a nonnegative coefficient in dimensions greater than four. Our result follows from unitarity of the spectral representation for a general ultraviolet completion of the GB term.
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…
In this paper we will consider quantum aspects of a non-local, infinite-derivative scalar field theory - a $\it toy \, model$ depiction of a covariant infinite-derivative, non-local extension of Einstein's general relativity which has previously been shown to be free from ghosts around the Minkowski background. The graviton propagator in this theory gets an exponential suppression making it $\it asymptotically \, free$, thus providing strong prospects of resolving various classical and quantum divergences. In particular, we will find that at $1$-loop, the $2$-point function is still divergent,…
We study ultraviolet cutoffs associated with the Weak Gravity Conjecture (WGC) and Sublattice Weak Gravity Conjecture (sLWGC). There is a magnetic WGC cutoff at the energy scale $e G_N^{-1/2}$ with an associated sLWGC tower of charged particles. A more fundamental cutoff is the scale at which gravity becomes strong and field theory breaks down entirely. By clarifying the nature of the sLWGC for nonabelian gauge groups we derive a parametric upper bound on this strong gravity scale for arbitrary gauge theories. Intriguingly, we show that in theories approximately saturating the sLWGC, the scale…
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.
We study various classical aspects of the Weyl transverse (WTDiff) gravity in a general space-time dimension. First of all, we clarify a classical equivalence among three kinds of gravitational theories, those are, the conformally-invariant scalar tensor gravity, Einstein's general relativity and the WTDiff gravity via the gauge fixing procedure. Secondly, we show that in the WTDiff gravity the cosmological constant is a mere integration constant as in unimodular gravity, but it does not receive any radiative corrections unlike the unimodular gravity. A key point in this proof is to construct …
In this paper we will show all the linearized curvature tensors in the infinite derivative ghost and singularity free theory of gravity in the static limit. We have found that in the region of non-locality, in the ultraviolet regime (at short distance from the source), the Ricci tensor and the Ricci scalar are not vanishing, meaning that we do not have a vacuum solution anymore due to the smearing of the source induced by the presence of non-local gravitational interactions. It also follows that, unlike in Einstein's gravity, the Riemann tensor is not traceless and it does not coincide with th…
Recent computations of scattering amplitudes show that N=8 supergravity is surprisingly well behaved in the ultraviolet and may even be ultraviolet finite in perturbation theory. The novel cancellations necessary for ultraviolet finiteness first appear at one loop in the guise of the "no-triangle hypothesis". We study one-loop amplitudes in pure Einstein gravity and point out the existence of cancellations similar to those found previously in N=8 supergravity. These cancellations go beyond those found in the one-loop effective action. Using unitarity, this suggests that generic theories of qua…
In modified gravity, the one-loop matter power spectrum exhibits an ultraviolet divergence as shown in the framework of the degenerate higher-order scalar-tensor theory. To address this problem, we extend the effective field theory of large scale structure to modified gravity theories. We find that new counterterms appear and renormalize the ultraviolet divergence as a natural consequence of non-linearity in the modified Poisson equation. The renormalized one-loop matter power spectrum is useful to test modified gravity theories by comparing to observations.
We generalize the ultraviolet sector of gravitation via a Born-Infeld action using lessons from massive gravity. The theory contains all of the elementary symmetric polynomials and is treated in the Palatini formalism. We show how the connection can be solved algebraically to be the Levi-Civita connection of an effective metric. The non-linearity of the algebraic equations yields several branches, one of which always reduces to General Relativity at low curvatures. We explore in detail a {\it minimal} version of the theory, for which we study solutions in the presence of a perfect fluid with s…
We explore the hypothesis that the set of symmetries enjoyed by the theory that describes gravity is not the full group of diffeomorphisms Diff(M), as in General Relativity, but a maximal subgroup of it, TransverseDiff(M), with its elements having a jacobian equal to unity; at the infinitesimal level, the parameter describing the coordinate change, xi^mu (x), is transverse, i.e., partial_mu(xi^mu)=0. Incidentally, this is the smaller symmetry one needs to propagate consistently a graviton, which is a great theoretical motivation for considering these theories. Also, the determinant of the metr…
Ultraviolet fixed point functions of the functional renormalisation group equation for $f(R)$-gravity coupled to matter fields are discussed. The metric is split via the exponential parameterisation into a background and a fluctuating metric, the former is chosen to be the one of a four-sphere. Also when scalar, fermion and vector fields are included global quadratic solutions exist as in the pure gravity case for discrete sets of values for some endomorphism parameters defining the coarse-graining scheme. The asymptotic, large-curvature behaviour of the fixed point functions is analysed for g…
In this work we investigate the ultraviolet behavior of Euclidean four-derivative quantum gravity beyond perturbation theory. In addition to a perturbative fixed point, we find an ultraviolet fixed point that is non-trivial in all couplings and is described by only two free parameters. This result is in line with the asymptotic safety scenario in quantum gravity. In particular, it supports the conjecture that the full theory is described by a finite number of free parameters.
We investigate the connection between Gravity's Rainbow and Horava-Lifshitz gravity, since both theories incorporate a modification in the UltraViolet regime which improves their quantum behavior at the cost of the Lorentz invariance loss. In particular, extracting the Wheeler-De Witt equations of the two theories in the case of Friedmann-Lemaitre-Robertson-Walker and spherically symmetric geometries, we establish a correspondence that bridges them.
We demonstrate that loop integrands of (super-)gravity scattering amplitudes possess surprising properties in the ultraviolet (UV) region. In particular, we study the scaling of multi-particle unitarity cuts for asymptotically large momenta and expose an improved UV behavior of four-dimensional cuts through seven loops as compared to standard expectations. For N=8 supergravity, we show that the improved large momentum scaling combined with the behavior of the integrand under BCFW deformations of external kinematics uniquely fixes the loop integrands in a number of non-trivial cases. In the int…
