Calculations In Quantum Gravity Research Articles

Naturally small neutrino mass with asymptotic safety and gravitational-wave signatures

We revisit the dynamical generation of an arbitrarily small neutrino Yukawa coupling in the Standard Model with trans-Planckian asymptotic safety and apply the same mechanism to the gauged B − L model. We show that thanks to the presence of additional irrelevant couplings, the described neutrino-mass generation in the B − L model is potentially more in line with existing theoretical calculations in quantum gravity. Interestingly, the model can accommodate, in full naturalness and without extensions, the possibility of purely Dirac, pseudo-Dirac, and Majorana neutrinos with any see-saw scale. We investigate eventual distinctive signatures of these cases in the detection of gravitational waves from first-order phase transitions. We find that, while it is easy to produce a signal observable in new-generation space interferometers, its discriminating features are washed out by the strong dependence of the gravitational-wave spectrum on the relevant parameters of the scalar potential.

INCONSISTENCIES FROM A RUNNING COSMOLOGICAL CONSTANT

We examine the general issue of whether a scale dependent cosmological constant can be consistent with general covariance, a problem that arises naturally in the treatment of quantum gravitation, where coupling constants generally run as a consequence of renormalization group effects. The issue is approached from several points of view, which include the manifestly covariant functional integral formulation, covariant continuum perturbation theory about two dimensions, the lattice formulation of gravity, and the nonlocal effective action and effective field equation methods. In all cases we find that the cosmological constant cannot run with scale, unless general covariance is explicitly broken by the regularization procedure. Our results are expected to have some bearing on current quantum gravity calculations, but more generally should apply to phenomenological approaches to the cosmological vacuum energy problem.

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.

Isolated and Dynamical Horizons and Their Applications.

Over the past three decades, black holes have played an important role in quantum gravity, mathematical physics, numerical relativity and gravitational wave phenomenology. However, conceptual settings and mathematical models used to discuss them have varied considerably from one area to another. Over the last five years a new, quasi-local framework was introduced to analyze diverse facets of black holes in a unified manner. In this framework, evolving black holes are modelled by dynamical horizons and black holes in equilibrium by isolated horizons. We review basic properties of these horizons and summarize applications to mathematical physics, numerical relativity, and quantum gravity. This paradigm has led to significant generalizations of several results in black hole physics. Specifically, it has introduced a more physical setting for black hole thermodynamics and for black hole entropy calculations in quantum gravity, suggested a phenomenological model for hairy black holes, provided novel techniques to extract physics from numerical simulations, and led to new laws governing the dynamics of black holes in exact general relativity.

One-loop calculations in quantumgravity: graviton self-energy, perturbative gauge invariance and Slavnov-Wardidentities

In this paper we calculate the one-loop graviton self-energy within theframework of causal perturbation theory. Because of thisregularization/renormalization scheme, the result is ultraviolet finite,without introducing counterterms, and cut-off-free. In addition, it satisfiesthe gravitational Slavnov-Ward identities for the two-point connectedGreen function. The latter are also investigated from the point of viewof a perturbative formulation of operator gauge invariance. Then, thecondition of perturbative gauge invariance to second order for loop graphsis proved. Corrections to the Newtonian potential coming from thegraviton self-energy are also derived.

Further uses of the quantum mechanical path integral in quantum field theory

It has been shown how matrix elements of the form 〈x‖exp(−iHt)‖y〉 which arise when using operator regularization to do perturbative calculations in quantum field theory can be evaluated using the quantum mechanical path integral (QMPI). This technique has the advantage of eliminating loop momentum integrals and algebraically complicated vertices in gauge theories. A similar (but distinct) approach of Polyakov and Strassler has been applied to one loop processes with external vector particles and is related to the string based methods of Bern and Kosower. In this article, several features of the QMPI technique are examined. First, it is demonstrated how the path ordering in the QMPI can be handled by considering a model of three interacting scalar fields, each with a distinct mass. Next, it is shown how the QMPI can be used when the external wave function is not a plane wave field. The particular case of having an exponentially damped wave function is considered. Next, a discussion of the difference between the approach of Polyakov and Strassler and that employed here is given. Finally, it is demonstrated how the QMPI can be used to considerably simplify calculations in quantum gravity.

Higher derivative quantum gravity on a simplicial lattice

We generalize the action of Regge calculus to include the equivalent to both a cosmological constant term and a higher derivative term involving the integral of R 2. We compare our expression for these terms with the continuum values for the regular tessellations of 2-, 3- and 4-dimensional spheres, and describe how the formalism may be applied to calculations in quantum gravity.

An ambiguity in one-loop quantum gravity

It is argued that the application of the dimensional regularisation technique to one-loop quantum gravity calculations is ambiguous. However, for the calculation of on-mass-shell S-matrix elements, this ambiguity can be resolved by requiring consistency with results obtained from other regularisation schemes. Some discussion is also given of the implications of this work for recent attempts to use higher derivative Lagrangians to solve the renormalisability problem in quantum gravity.