One-loop Quantum Gravity Research Articles

Worldline path integrals for the graviton

We present an extension to arbitrary dimensions of a worldline path integral approach to one-loop quantum gravity, which was previously formulated in four spacetime dimensions. By utilizing this method, we recalculate gauge invariant coefficients related to the UV divergences of quantum gravity. These gauge invariant coefficients were previously obtained in arbitrary dimensions through two alternative techniques: the quantization of the N=4 spinning particle that propagates the graviton on Einstein spaces and the more conventional heat kernel approach. Our worldline path integrals are closer to the latter method and are employed to compute the trace of the heat kernel.

Vacuum polarization in the cosmic-string background

Within the framework of one-loop quantum gravity, we consider the vacuum polarization effect of the minimally-coupled massive scalar field near the infinitely-thin straight cosmic string. It is shown that the massive-field relative contribution to the renormalized vacuum mean of the energy density becomes negligible at a distance of several Compton lengths.

Gravity Loop Corrections to the Standard Model Higgs in Einstein Gravity

We study one-loop quantum gravity corrections to the standard model Higgs potential \(V(\phi) \grave{\rm a}\) la Coleman-Weinberg and examine the stability question of \(V(\phi) \) in the energy region of Planck mass scale, \(\mu\simeq M_{\rm Pl}\) \((M_{\rm Pl}=1.22\times10^{19}{\rm GeV})\). We calculate the gravity one-loop corrections to \(V(\phi)\) in Einstein gravity by using the momentum cut-off \(\Lambda\). We have found that even small gravity corrections compete with the standard model term of \(V(\phi)\) and affect the stability argument of the latter part alone. This is because the latter part is nearly zero in the energy region of \(M_{\rm Pl}\).

Dark energy and inflation in a gravitational wave dominated universe

The empty space (with no matter fields) is not really empty because of natural metric fluctuations, quantum and classical. We show that gravitons as well as classical gravitational waves of super-horizon wavelengths are able to form the de Sitter state of the empty homogeneous isotropic Universe. This state is the exact solution to the self-consistent equations of one-loop quantum gravity for gravitons in the empty FLRW space. It also is the exact solution to the self-consistent equations of back reaction for classical gravitational waves. Technically, to get this de Sitter solution in both quantum and classical cases, it is necessary to make the transition to imaginary time and then come back to real time which is possible because this de Sitter state is invariant with respect to Wick rotation. Such a procedure means that the time was used as a complex variable, and this fact has a deep but still not understood meaning. De Sitter accelerated expansion of the empty Universe naturally explains the origin of dark energy and inflation because the Universe is empty at the start and by the end of its evolution. This theory is consistent with the existing observational data. The CMB anisotropy of the order of 10^-5 is produced by fluctuations in the number of gravitons. The existence of a threshold and unique coincidence of topologically impenetrable barriers for tunneling takes place for the matter-dominated epoch and De Sitter State only. These facts provide a solution to the coincidence problem. The theoretical prediction that the equation-of-state parameter should be w>-1 for inflation and w<-1 for dark energy is consistent with observational data. To provide the reader with a complete picture, this paper gather together new and some published results of the graviton theory of the origin of inflation and dark energy

Inflation and CMB anisotropy from quantum metric fluctuations

We propose a model of cosmological evolution of the early and late Universe which is consistent with observational data and naturally explains the origin of inflation and dark energy. We show that the de Sitter accelerated expansion of the FLRW space with no matter fields (hereinafter, empty space) is its natural state, and the model does not require either a scalar field or cosmological constant or any other hypotheses. This is due to the fact that the De Sitter State is an exact solution of the rigorous mathematically consistent equations of one-loop quantum gravity for the empty FLRW space that are finite off the mass shell. Space without matter fields is not empty as it always has the natural quantum fluctuations of the metric, i.e. gravitons. Therefore, the empty (in this sense) space is filled with gravitons, which have the backreaction effect on its evolution over time forming a self-consistent de Sitter instanton leading to the exponentially accelerated expansion of the Universe. At the start and the end of cosmological evolution, the Universe is assumed to be empty, and this fact explains the origin of inflation and dark energy. The Universe starts and ends with de Sitter expansion but the evolutionary process runs in these cases in opposite directions. It leads to the prediction that the signs of the parameter 1 + w should be opposite in the two cases, which is consistent with observations. Fluctuations of the number of gravitons lead to fluctuations of their energy density which in turn leads to the observed CMB temperature anisotropy of the order of ∼10−5 and CMB polarization. Within this scenario, it is not a hypothetical scalar field that generates inflation and relic gravitational waves but on the contrary, gravitational waves (gravitons) generate inflation, CMB anisotropy and dark energy.

Quantum gravity corrections to the conformally coupled scalar self-mass-squared on de Sitter background

We evaluate one-loop quantum gravity corrections to the conformally coupled (CC) scalar self-mass-squared on a locally de Sitter background. In this paper we consider only the conformal-conformal interaction part of the self-mass-squared. This complements the minimal-minimal part worked out in the previous paper [E. O. Kahya and R. P. Woodard, Phys. Rev. D 76, 124005 (2007)], and we add the minimal-conformal part in a follow-up paper to complete the full self-mass-squared at one-loop order. The computation is performed using dimensional regularization, and the results are fully renormalized by absorbing divergences with counterterms. The finite results can give rise to quantum corrections to the CC scalar mode functions and therefore to their power spectra.

A one-loop test of quantum supergravity

The partition function on the three-sphere of ABJM theory and its generalizations has, at large N, a universal, subleading logarithmic term. Inspired by the success of one-loop quantum gravity for computing the logarithmic corrections to black hole entropy, we try to reproduce this universal term by a one-loop calculation in Euclidean 11-dimensional supergravity on AdS4 × X7. We find perfect agreement between the results of ABJM theory and the 11-dimensional supergravity.

One-loop quantum gravity from a worldline viewpoint

We develop a worldline approach to quantum gravity in D = 4. Using the background field method we consider the covariantly gauge fixed Einstein-Hilbert action with cosmological constant, and find a worldline representation of the differential operators identified by its quadratic approximation. We test it by computing the correct one-loop divergencies. Alternative worldline methods, such as the use of the O(4) spinning particle that is known to describe correctly the propagation of a massless spin 2 particle in D = 4, find obstructions in the coupling to an arbitrary background metric, apparently preventing a more extensive use in perturbative descriptions of quantum gravity. We expect that our model might simplify calculations of one-loop amplitudes with respect to standard quantum field theoretical methods.

Macroscopic Effect of Quantum Gravity: Graviton, Ghost and Instanton Condensation on Horizon Scale of Universe

We discuss a special class of quantum gravity phenomena that occur on the scale of the Universe as a whole at any stage of its evolution, including the contemporary Universe. These phenomena are a direct consequence of the zero rest mass of gravitons, conformal non-invariance of the graviton field, and one-loop finiteness of quantum gravity, i.e. it is a direct consequence of first principles only. The effects are due to graviton-ghost condensates arising from the interfereence of quantum coherent states. Each of coherent states is a state of gravitons and ghosts of a wavelength of the order of the horizon scale and of different occupation numbers. The state vector of the Universe is a coherent superposition of vectors of different occupation numbers. One-loop approximation of quantum gravity is believed to be applicable to the contemporary Universe because of its remoteness from the Planck epoch. To substantiate the reliability of macroscopic quantum effects, the formalism of one-loop quantum gravity is discussed in detail. The theory is constructed as follows: Faddeev-Popov path integral in Hamilton gauge → factorization of classical and quantum variables, allowing the existence of a self-consistent system of equations for gravitons, ghosts and macroscopic geometry → transition to the one-loop approximation, taking into account that contributions of ghost fields to observables cannot be eliminated in any way. The ghost sector corresponding to the Hamilton gauge automatically ensures of one-loop finiteness of the theory off the mass shell. The Bogolyubov-Born-Green-Kirckwood-Yvon (BBGKY) chain for the spectral function of gravitons renormalized by ghosts is used to build a self-consistent theory of gravitons in the isotropic Universe. It is the first use of this technique in quantum gravity calculations. We found three exact solutions of the equations, consisting of BBGKY chain and macroscopic Einstein’s equations. It was found that these solutions describe virtual graviton and ghost condensates as well as condensates of instanton fluctuations. All exact solutions, originally found by the BBGKY formalism, are reproduced at the level of exact solutions for field operators and state vectors. It was found that exact solutions correspond to various condensates with different graviton-ghost compositions. Each exact solution corresponds to a certain phase state of graviton-ghost substratum. We establish conditions under which a continuous quantum-gravity phase transitions occur between different phases of the graviton-ghost condensate.

One-Loop Quantum Gravity Repulsion in the Early Universe

Perturbative quantum gravity formalism is applied to compute the lowest order corrections to the classical spatially flat cosmological Friedmann-Lemaître-Robertson-Walker solution (for the radiation). The presented approach is analogous to the approach applied to compute quantum corrections to the Coulomb potential in electrodynamics, or rather to the approach applied to compute quantum corrections to the Schwarzschild solution in gravity. In the framework of the standard perturbative quantum gravity, it is shown that the corrections to the classical deceleration, coming from the one-loop graviton vacuum polarization (self-energy), have (UV cutoff free) opposite to the classical repulsive properties which are not negligible in the very early Universe. The repulsive "quantum forces" resemble those known from loop quantum cosmology.

Secular effects on inflation from one-loop quantum gravity

In this Letter we revisit and extend a previous analysis where the possible relevance of quantum gravity effects in a cosmological setup was studied. The object of interest are non-local (logarithmic) terms generated in the effective action of gravity due to the exchange in loops of massless modes (such as photons or the gravitons themselves). We correct one mistake existing in the previous work and discuss the issue in a more general setting in different cosmological scenarios. We obtain the one-loop quantum-corrected evolution equations for the cosmological scale factor up to a given order in a derivative expansion in two particular cases: a matter dominated universe with vanishing cosmological constant, and in a de Sitter universe. We show that the quantum corrections, albeit tiny, may have a secular effect that eventually modifies the expansion rate. For a de Sitter universe they tend to slow down the rate of the expansion, while the effect may be the opposite in a matter dominated universe.

Cosmological Acceleration from Virtual Gravitons

Intrinsic properties of the space itself and quantum fluctuations of its geometry are sufficient to provide a mechanism for the acceleration of cosmological expansion (dark energy effect). Applying Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy approach to self-consistent equations of one-loop quantum gravity, we found exact solutions that yield acceleration. The permanent creation and annihilation of virtual gravitons is not in exact balance because of the expansion of the Universe. The excess energy comes from the spontaneous process of graviton creation and is trapped by the background. It provides the macroscopic quantum effect of cosmic acceleration.

Irreducible forms for the metric variations of the action terms of sixth-order gravity and approximated stress–energy tensor

We provide irreducible expressions for the metric variations of the gravitational action terms constructed from the 17 curvature invariants of order six in the derivatives of the metric tensor, i.e., from the geometrical terms appearing in the diagonal heat-kernel or Gilkey–DeWitt coefficient a3. We then express, for a four-dimensional spacetime, the approximated stress–energy tensor constructed from the renormalized DeWitt–Schwinger effective action associated with a massive scalar field. We also construct, for higher dimensional spacetimes, the infinite counterterms of order six in the derivatives of the metric tensor appearing on the left-hand side of Einstein equations as well as the contribution associated with the cubic Lovelock gravitational action. In the appendix, we provide a list of geometrical relations we have used and which are more generally helpful for calculations in two-loop quantum gravity in a four-dimensional background or for calculations in one-loop quantum gravity in higher dimensional background. We also obtain the approximated stress–energy tensors associated with a massive spinor field and a massive vector field propagating in a four-dimensional background.

BOUNDARY OPERATORS IN QUANTUM FIELD THEORY

The fundamental laws of physics can be derived from the requirement of invariance under suitable classes of transformations on the one hand, and from the need for a well-posed mathematical theory on the other hand. As a part of this programme, the present paper shows under which conditions the introduction of pseudodifferential boundary operators in one-loop Euclidean quantum gravity is compatible both with their invariance under infinitesimal diffeomorphisms and with the requirement of a strongly elliptic theory. Suitable assumptions on the kernel of the boundary operator make it therefore possible to overcome problems resulting from the choice of purely local boundary conditions.

GRAVITATIONAL THERMODYNAMICS OF SPACETIME FOAM IN ONE-LOOP APPROXIMATION

We show from one-loop quantum gravity and statistical thermodynamics that the thermodynamics of quantum foam in flat spacetime and Schwarzschild spacetime is exactly the same as that of Hawking–Unruh radiation in thermal equilibrium. This means we show unambiguously that Hawking–Unruh thermal radiation should contain thermal gravitons or the contribution of quantum spacetime foam. As a by-product, we give also the quantum gravity correction in one-loop approximation to the classical black hole thermodynamics.

Gauge-Invariant and Gauge-Fixing Independent Effective Action in One-Loop Quantum Gravity

The one-parameter dependent family of the gauge invariant and gauge fixing independent effective actions is considered in one-loop approximation. The one-loop unique effective action (chosing as the representative of this family) in d = 4 Einstein quantum gravity with scalar field and Brans-Dicke quantum theory in flat space, in d = 4 Einstein gravity on De Sitter background, in higher derivative gravity on d-dimensional torus compactified background is calculated. The configuration-space metric dependence of the unique effective action in these calculations is investigated. The appearing problems (the configuration-space metric dependence of the physical quantities like induced gravitational constant) are discussed.

Gauge-Invariant and Gauge-Fixing Independent Effective Action in One-Loop Quantum Gravity

The one-parameter dependent family of the gauge invariant and gauge fixing independent effective actions is considered in one-loop approximation. The one-loop unique effective action (chosing as the representative of this family) in d = 4 Einstein quantum gravity with scalar field and Brans-Dicke quantum theory in flat space, in d = 4 Einstein gravity on De Sitter background, in higher derivative gravity on d-dimensional torus compactified background is calculated. The configuration-space metric dependence of the unique effective action in these calculations is investigated. The appearing problems (the configuration-space metric dependence of the physical quantities like induced gravitational constant) are discussed.

The path integral measure, conformal factor problem and stability of the ground state of quantum gravity

The functional measure for the Feynman path integral over four-geometries is constructed by the same generally covariant methods used by Polyakov for string theory. Ultralocality and general covariance determine the gaussian measure almost uniquely, and lead to a jacobian factor in the path integral which is just that required to render the linearized conformal perturbations (σ) of any Ricci-flat background into non-propagating, constrained modes. The non-trivial jacobian in the measure is equivalent to the non-local field redefinition χ = √−▽ 2 σ. It is the euclidean continuation of χ (rather than σ) which leads to a completely convergent euclidean path integral, consistent with unitarity. Thus, the conformal factor problem in one-loop euclidean quantum gravity is understood to be an artifact of the naive analytic continuation of the Einstein-Hilbert action. We reconsider the issue of the ground state of quantum gravity in light of this result, and show that flat space-time is absolutely stable to gaussian quantum fluctuations in the infrared. The extension of the method to non-Ricci-flat backgrounds is discussed as well.

Quenching the cosmological constant

Abstract We propose and try to justify a model - inspired by known features of one-loop quantum gravity corrections - in which the effective cosmological constant is consistent with inflationary needs at early times and sufficiently suppressed at later epochs.

On the new definition of off-shell effective action

We analyze the recently proposed definition of the off-shell, gauge-invariant, gauge-independent, effective action Γ , utilizing an invariant metric on the field space. It is shown how to establish correspondence between Γ and the standard effective action, calculated in some particular (Landau-type) gauge. Several examples are explicitly discussed, including Yang-Mills theory, the effective potential in scalar QED, and one-loop quantum gravity. Generalization to the case of super-invariant theories (e.g. super-Yang-Mills and supergravity) is also presented.