Action Of Quantum Gravity Research Articles

Matching the Vilkovisky–DeWitt Effective Action of Quantum Gravity to String Theory

AbstractIn this work, the matching of the Vilkovisky–DeWitt effective action of quantum gravity is discussedwith an example of an ultra‐violet complete theory of quantum gravity. The authors show how this matching enables a calculation of the local Wilson coefficients of the effective action. Several examples in string theory are provided. Moreover, the matching conditions within the context of the swampland program are discussed.

Probing Gauss-Bonnet-corrected inflation with gravitational waves

The low energy effective action of quantum gravity may include the higher curvature terms such as the Gauss-Bonnet term.The inflaton dynamics may be affected by the Gauss-Bonnet term if there is an inflaton-Gauss-Bonnet coupling.We show that an inflation model with a simple power law potential is made viable if it is coupled to the Gauss-Bonnet term since the prediction on the scalar spectral index and the tensor-to-scalar ratio are modified.We further point out that such a model predicts huge amount of gravitational waves at the high frequency range around 100 GHz–100 THz through the perturbative inflaton decay into gravitons induced by the Gauss-Bonnet term.Thus the spectrum of high frequency gravitational background is a unique feature of the inflation models with a Gauss-Bonnet correction.

An approximate application of quantum gravity to the rotation problem

Arbitrary initial conditions allow solutions of Einstein’s field equations for General Relativity to have arbitrarily large relative rotation of matter and inertial frames. The ‘Rotation Problem’ is to explain why the measured relative rotation rate is so small. As it turns out, nearly any reasonable theory of quantum gravity can solve the rotation problem by phase interference. Even as early as about a quarter of a second after the initial simgularity, quantum cosmology would limit the cosmologies that contribute significantly to a path integral calculation to have relative rms rotation rates less than about 10−51 radians per year. Those calculations are based on using 50 e-foldings during inflation. For 55 or 60 e-foldings, the cosmologies contributing significantly to the path integral would have even smaller relative rotation rates. In addition, although inflation dominates the calculation, even if there had been no inflation, the cosmologies contributing significantly to the path integral would have relative rotation rates less than about 10−32 radians per year at about a quarter of a second after the initial singularity. These calculations are insensitive to the details of the theory of quantum gravity because the main factor depends only on the size of the visible Universe, the Planck time, the free-space speed of light, the Hubble parameter, and the number of e-foldings during inflation. These calculations use the Einstein–Hilbert action in quantum gravity, including large-scale relative rotation of inertial frames and the matter distribution, in which each ‘path’ is a cosmology with a different rms relative rotation rate. The calculations include inflation for 50, 55, and 60 e-foldings, and for values of the dependence of relative rotation rate on cosmological scale factor a as a −m for various values of m. The calculation shows that the action is an extremum at zero rms relative rotation rate.

Six-dimensional one-loop divergences in quantum gravity from the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 spinning particle

In this work, we investigate the computation of the counterterms necessary for the renormalization of the one-loop effective action of quantum gravity using both the worldline formalism and the heat kernel method. Our primary contribution is the determination of the Seleey-DeWitt coefficient a3(D) for perturbative quantum gravity with a cosmological constant, which we evaluate on Einstein manifolds of arbitrary D dimensions. This coefficient characterizes quantum gravity in a gauge-invariant manner due to the on-shell condition of the background on which the graviton propagates. Previously, this coefficient was not fully known in the literature. We employ the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 spinning particle model recently proposed to describe the graviton in first quantization and then use the heat kernel method to cross-check the correctness of our calculations. Finally, we restrict to six dimensions, where the coefficient corresponds to the logarithmic divergences of the effective action, and compare our results with those available in the literature.

Dynamical dark energy and infinite statistics

In the [Formula: see text]CDM model, dark energy is viewed as a constant vacuum energy density, the cosmological constant in the Einstein–Hilbert action. This assumption can be relaxed in various models that introduce a dynamical dark energy. In this paper, we argue that the mixing between infrared (IR) and ultraviolet (UV) degrees of freedom in quantum gravity leads to infinite statistics, the unique statistics consistent with Lorentz invariance in the presence of nonlocality, and yields a fine structure for dark energy. Introducing IR and UV cutoffs into the quantum gravity action, we deduce the form of [Formula: see text] as a function of redshift and translate this to the behavior of the Hubble parameter.

Effective action, spectrum and first law of wedge holography

In this paper, we study the effective action, the mass spectrum and the first law of entanglement entropy for a novel doubly holographic model called wedge holography. We work out the effective action of quantum gravity on the branes. In the perturbative formulation, it is given by an infinite sum of Pauli-Fierz actions. In the non-perturbative formulation, the effective action is composed of a higher derivative gravity and a matter action. Usually, a higher derivative gravity can be renormalizable but suffers the ghost problem. For our case, since the effective theory on the brane is equivalent to Einstein gravity in the bulk, it must be ghost-free. We notice that the matter action plays an important role in eliminating the ghost. We also provide evidences that the higher derivative gravity on the brane is equivalent to a ghost-free multi-gravity. Besides, we prove that the effective action yields the correct Weyl anomaly. Interestingly, although the effective action on the brane is an infinite tower of higher derivative gravity, the holographic Weyl anomaly is exactly the same as that of Einstein gravity. We also analyze the mass spectrum of wedge holography. Remarkably, there is always a massless mode of gravitons on the end-of-the-world branes in wedge holography. This happens because one imposes Neumann boundary condition on both branes. On the other hand, the massless mode disappears if one imposes Dirichlet boundary condition on one of the branes as in brane world theory and AdS/BCFT. Finally, we verify the first law of entanglement entropy for wedge holography. Interestingly, the massive fluctuations are irrelevant to the first order perturbation of the holographic entanglement entropy. Thus, in many aspects, the effective theory on the brane behaves like massless Einstein gravity.

Quantum gravitational corrections to the entropy of a Reissner–Nordström black hole

Starting from an effective action for quantum gravity, we calculate the quantum gravitational corrections to the Wald entropy of a four dimensional non-extremal Reissner–Nordström (RN) black hole in the limit of small electric charge, generalising a previous calculation carried out by Calmet and Kuipers (Phys Rev D 104(6):066012, 2021) for a Schwarzschild black hole. We show that, at second order in the Ricci curvature, the RN metric receives quantum corrections which shift the classical position of the event horizon. We apply the Wald entropy formula by integrating over the perimeter of the quantum corrected event horizon. We then compute the quantum gravitational corrections to the temperature and the pressure of the black hole.

Metrics with Zero and Almost-Zero Einstein Action in Quantum Gravity

We generate numerically on a lattice an ensemble of stationary metrics, with spherical symmetry, which have Einstein action SE « ћ. This is obtained through a Metropolis algorithm with weight exp(−β2S2E) and β » ћ−1. The squared action in the exponential allows to circumvene the problem of the non-positivity of SE. The discretized metrics obtained exhibit a spontaneous polarization in regions of positive and negative scalar curvature. We compare this ensemble with a class of continuous metrics previously found, which satisfy the condition SE = 0 exactly, or in certain cases even the stronger condition R(x) = 0 for any x. All these gravitational field configurations are of considerable interest in quantum gravity, because they represent possible vacuum fluctuations and are markedly different from Wheeler’s “spacetime foam”.

Background independent quantum field theory and gravitating vacuum fluctuations

The scale dependent effective average action for quantum gravity complies with the fundamental principle of Background Independence. Ultimately the background metric it formally depends on is selected self-consistently by means of a tadpole condition, a generalization of Einstein’s equation. Self-consistent background spacetimes are scale dependent, and therefore “going on-shell” at the points along a given renormalization group (RG) trajectory requires understanding two types of scale dependencies: the (familiar) direct one carried by the off-shell action functional, and an equally important indirect one related to the continual re-adjustment of the background geometry. This paper is devoted to a careful delineation and analysis of certain general questions concerning the indirect scale dependence, as well as a detailed explicit investigation of the case where the self-consistent metrics are determined predominantly by the RG running of the cosmological constant. Mathematically, the object of interest is the spectral flow induced by the background Laplacian which, on-shell, acquires an explicit scale dependence. Among other things, it encodes the complete information about the specific set of field modes which, at any given scale, are the degrees of freedom constituting the respective effective field theory. For a large class of RG trajectories (Type IIIa) we discover a seemingly paradoxical behavior that differs substantially from the off-shell based expectations: A Background Independent theory of (matter coupled) quantum gravity looses rather than gains degrees of freedom at increasing energies. As an application, we investigate to what extent it is possible to reformulate the exact theory in terms of matter and gravity fluctuations on a rigid flat space. It turns out that, in vacuo, this “rigid picture” breaks down after a very short RG time already (less than one decade of scales) because of a “scale horizon” that forms. Furthermore, we critically reanalyze and refute the frequent claim that the huge energy densities one obtains in standard quantum field theory by summing up to zero-point energies imply a naturalness problem for the observed small value of the cosmological constant.

Coadjoint orbit action of Virasoro group and two-dimensional quantum gravity dual to SYK/tensor models

The Nambu-Goldstone (NG) bosons of the SYK model are described by a coset space Diff/SL(2, ℝ), where Diff, or Virasoro group, is the group of diffeomorphisms of the time coordinate valued on the real line or a circle. It is known that the coadjoint orbit action of Diff naturally turns out to be the two-dimensional quantum gravity action of Polyakov without cosmological constant, in a certain gauge, in an asymptotically flat spacetime. Motivated by this observation, we explore Polyakov action with cosmological constant and boundary terms, and study the possibility of such a two-dimensional quantum gravity model being the AdS dual to the low energy (NG) sector of the SYK model. We find strong evidences for this duality: (a) the bulk action admits an exact family of asymptotically AdS2 spacetimes, parameterized by Diff/SL(2, ℝ), in addition to a fixed conformal factor of a simple functional form; (b) the bulk path integral reduces to a path integral over Diff/SL(2, ℝ) with a Schwarzian action; (c) the low temperature free energy qualitatively agrees with that of the SYK model. We show, up to quadratic order, how to couple an infinite series of bulk scalars to the Polyakov model and show that it reproduces the coupling of the higher modes of the SYK model with the NG bosons.

Beyond-one-loop quantum gravity action yielding both inflation and late-time acceleration

A unified description of early-time inflation with the current cosmic acceleration is achieved by means of a new theory that uses a quadratic model of gravity, with the inclusion of an exponential F(R)-gravity contribution for dark energy. High-curvature corrections of the theory come from higher-derivative quantum gravity and yield an effective action that goes beyond the one-loop approximation. It is shown that, in this theory, viable inflation emerges in a natural way, leading to a spectral index and tensor-to-scalar ratio that are in perfect agreement with the most reliable Planck results. At low energy, late-time accelerated expansion takes place. As exponential gravity, for dark energy, must be stabilized during the matter and radiation eras, we introduce a curing term in order to avoid nonphysical singularities in the effective equation of state parameter. The results of our analysis are confirmed by accurate numerical simulations, which show that our model does fit the most recent cosmological data for dark energy very precisely.

Quantum gravity and renormalization

The properties of quantum gravity are reviewed from the point of view of renormalization. Various attempts to overcome the problem of non-renormalizability are presented, and the reasons why most of them fail for quantum gravity are discussed. Interesting possibilities come from relaxing the locality assumption, which also can inspire the investigation of a largely unexplored sector of quantum field theory. Another possibility is to work with infinitely many independent couplings, and search for physical quantities that only depend on a finite subset of them. In this spirit, it is useful to organize the classical action of quantum gravity, determined by renormalization, in a convenient way. Taking advantage of perturbative local field redefinitions, we write the action as the sum of the Hilbert term, the cosmological term, a peculiar scalar that is important only in higher dimensions, plus invariants constructed with at least three Weyl tensors. We show that the FRLW configurations, and many other locally conformally flat metrics, are exact solutions of the field equations in arbitrary dimensions d>3. If the metric is expanded around such configurations the quadratic part of the action is free of higher-time derivatives. Other well-known metrics, such as those of black holes, are instead affected in nontrivial ways by the classical corrections of quantum origin.

Discussion on possible effects of the Barbero-Immirzi parameter at the TeV-scale particle physics

In this paper, we analyze a curvature- and torsion-square quantum gravity action with an additional Holst term minimally coupled to a massive Dirac field in four dimensions. The main purpose here is to try to estimate and compare the value of the Barbero-Immirzi parameter with its currently known results. To do that, we work out the physical mass of the fermion as a function of this parameter in a perturbative one-loop calculation, assuming the scenario of a physics at the TeV scale.

Properties of the classical action of quantum gravity

The classical action of quantum gravity, determined by renormalization, contains infinitely many independent couplings and can be expressed in different perturbatively equivalent ways. We organize it in a convenient form, which is based on invariants constructed with the Weyl tensor. We show that the FLRW metrics are exact solutions of the field equations in arbitrary dimensions, and so are all locally conformally flat solutions of the Einstein equations. Moreover, expanding the metric tensor around locally conformally flat backgrounds the quadratic part of the action is free of higher derivatives. Black-hole solutions of Schwarzschild and Kerr type are modified in a non-trivial way. We work out the first corrections to their metrics and study their properties.

The Maxwell–Einstein system, Ward identities and the Vilkovisky construction

The gauge fixing dependence of the one-loop effective action of quantum gravity in the proper-time representation is investigated for a space of arbitrary curvature, and the investigation is extended to Maxwell–Einstein theory. The construction of Vilkovisky and DeWitt for removal of this dependence is then considered in general gauges, and it is shown that nontrivial criteria arising from a Ward identity of the theory must be obeyed by the regularization scheme, if the construction is to remove the gauge dependence of quadratic and quartic divergences. The results apply also to non-Abelian gauge theories; they are used to address the question of gauge dependence of asymptotic freedom arising through internal graviton lines at one-loop order as suggested by Robinson and Wilczek.

Renormalizable 4D Quantum Gravity as a Perturbed Theory from CFT

We study the renormalizable quantum gravity formulated as a perturbed theory from conformal field theory (CFT) on the basis of conformal gravity in four dimensions. The conformal mode in the metric field is managed non-perturbatively without introducing its own coupling constant so that conformal symmetry becomes exact quantum mechanically as a part of diffeomorphism invariance. The traceless tensor mode is handled in the perturbation with a dimensionless coupling constant indicating asymptotic freedom, which measures a degree of deviation from CFT. Higher order renormalization is carried out using dimensional regularization, in which the Wess-Zumino integrability condition is applied to reduce indefiniteness existing in higher-derivative actions. The effective action of quantum gravity improved by renormalization group is obtained. We then make clear that conformal anomalies are indispensable quantities to preserve diffeomorphism invariance. Anomalous scaling dimensions of the cosmological constant and the Planck mass are calculated. The effective cosmological constant is obtained in the large number limit of matter fields.

Seeking the loop quantum gravity Barbero-Immirzi parameter and field in 4D,N=1supergravity

We embed the loop quantum gravity Barbero-Immirzi parameter and field within an action describing 4D, $\mathcal{N}=1$ supergravity and thus within a low-energy effective action of superstring/M theory. We use the fully gauge-covariant description of supergravity in (curved) superspace. The gravitational constant is replaced with the vacuum expectation value of a scalar field, which in local supersymmetry is promoted to a complex, covariantly chiral scalar superfield. The imaginary part of this superfield couples to a supersymmetric Holst term. The Holst term also serves as a starting point in the loop quantum gravity action. This suggest the possibility of a relation between loop quantum gravity and supersymmetric string theory, where the Barbero-Immirzi parameter and field of the former play the role of the supersymmetric axion in the latter. Adding matter fermions in loop quantum gravity may require the extension of the Holst action through the Nieh-Yan topological invariant, while in pure, matter-free supergravity their supersymmetric extensions are the same. We show that, when the Barbero-Immirzi parameter is promoted to a field in the context of 4D supergravity, it is equivalent to adding a dynamical complex chiral (dilaton-axion) superfield with a nontrivial kinetic term (or K\ahler potential), coupled to supergravity.

Stabilized quantum gravity stochastic interpretation and numerical simulation

Following the reasoning of Claudson and Halpern, it is shown that “fifth-time” stabilized quantum gravity is equivalent to Langevin evolution (i.e. stochastic quantization) between fixed non-singular, but otherwise arbituary, initial and final states. The simple restriction to a fixed final state at t 5 → ∞ is sufficient to stabilize the theory. This equivalence fixes the integration measure, and suggests a particular operator-ordering, for the fifth-time action of quantum gravity. Results of a numerical simulation of stabilized, latticized Einstein-Cartan theory on some small lattices are reported. In the range of cosmological constant λ investigated, it is found that: (i) the system is always in the broken phase 〈det( e)〉 ≠ 0; and (ii) the negative free energy is large, possibly singular, in the vincinity of λ = 0. The second finding may be relevant to the cosmological-constant problem.

Effective action in quantum gravity

It is argued that the effective action theory may be regarded as a phenomenological theory describing a certain class of measurements irrespective of the nature of fundamental quantum objects. The effective action in quantum field theory is discussed in detail and used as a guide. A connection between the effective field and observables is established. The approach is applied to the gravitational collapse problem. A procedure for building a basis of non-local gravitational invariants is described and a result for the vacuum radiation in a spherically symmetric in-state is presented. A conclusion about breakdown of measurements at the Planck scale is revised.

The ϵ-expansion of two-dimensional quantum gravity

Motivated by recent suggestions that renormalisation constants evaluated at the fixed point of the ϵ-expansion for two-dimensional quantum gravity might reproduce Polyakov's exact two-dimensional results, we discuss the perturbative calculation of the effective action for quantum gravity in (2 − ϵ) dimensions. We show that the theory is non-renormalizable at two-loop order.