Effective Theory For Quantum Gravity Research Articles

Negative scalar potentials and the swampland: an Anti-Trans-Planckian Censorship Conjecture

In this paper, we derive a characterisation of negative scalar potentials, V < 0, in d-dimensional effective theories of quantum gravity. This is achieved thanks to an Anti-Trans-Planckian Censorship Conjecture (ATCC), inspired by a refined version of the TCC. The ATCC relies on the fact that in a contracting universe, modes that become sub-Planckian in length violate the validity of the effective theory. In the asymptotics of field space, we deduce that −V′/V ≥ c0 when V′ ≥ 0. The rate {c}_0=2/sqrt{left(d-1right)left(d-2right)} is successfully tested in several string compactifications for d ≥ 4. In addition, a new asymptotic condition, V′′/V ≥ {c}_0^2 , is derived. By extrapolation to anti-de Sitter solutions of radius l, we infer the existence of a scalar whose mass should obey m2l2 ≲ −2. This property is verified in many supersymmetric examples.

Self-adjoint extensions for a [formula omitted]-corrected Hamiltonian of a particle on a finite interval

In the present paper we deal with the issue of finding the self-adjoint extensions of a p4-corrected Hamiltonian. The importance of this subject lies on the application of the concepts of quantum mechanics to the minimal-length scale scenario which describes an effective theory of quantum gravity. We work in a finite one dimensional interval and we give the explicit U(4) parametrization that leads to the self-adjoint extensions. Once the parametrization is known, we can choose appropriate U(4) matrices to model physical problems. As examples, we discuss the infinite square-well, periodic conditions, anti-periodic conditions and periodic conditions up to a prescribed phase. We hope that the parametrization we found will contribute to model other interesting physical situations in further works.

Anisotropic noncommutative Schwarzschild metamaterial

The propagation of light through the metamaterial analogue to the Noncommutative Schwarzschild spacetime is studied. NonCommutative (NC) spacetime properties have been considered in several high energy theories which in the context of gravitation, those may be considered as effective theories of quantum gravity. Following the approach established in [6], we found the properties related to the metamaterial corresponding to the NC-Schwarzschild spacetime. The main effects observed in the simulations are a deviation in the light path and a difference in the electric field norm of the beam compared to the propagation in the standard Schwarzschild metamaterial. These measurable effects are useful to determine the existence of noncommutativity. Also, metamaterial simulations offer a novel way to explore possible observable consequences of modified theories of General Relativity.

Palatini Higgs inflation and the refined dS conjecture

The refined de Sitter derivative conjecture provides constraints to potentials that are low energy effective theories of quantum gravity. It can give direct bounds on inflationary scenarios and determine whether the theory is in the Landscape or the Swampland. Any infationary model can be checked by these conditions and non-minimally coupled scalar field theory is not an exception. We consider the Palatini Higgs inflation scenario taking the refined de Sitter derivative conjecture into account. According to the latest cosmological observations from Planck 2018, BICEP2+Keck and the bound of non-minimal coupling parameter {\xi}, we suggest that if the refined dS conjecture does indeed hold, then the Palatini Higgs inflation model cannot be the low energy effective theory of a consistent quantum gravity theory since the two parameters c1 and c2 are much smaller than order 1, which is inconsistent with the refined dS conjecture. Therefore we suggest that it is in the Swampland.

Indirect probe of quantum gravity using molecular wave-packets

The most obvious obstacle behind a direct test of quantum gravity (QG) is its energy scale (1019 GeV), which remains well outside of any human made machine. The next best possible approach is to provide indirect tests on effective theories of QG which can be performed in a lower energy scale. This paper is aimed in this direction, and shows a promising path to test the existence of the fundamental minimal length scale of Nature by measuring the dispersion of free, large molecular wave-packets. The existence of the minimal length is believed to be the reason for a modified commutation relationship between the position and momentum operators and, in this paper, we show that such a modification of the commutator has a profound effect on the dispersion rate of free wave-packets, and precise measurement on the broadening times of large molecular wave-packets (such as C60, C176 and large organic molecules) provide a promising path for an indirect test of quantum gravity, in a laboratory setting.

The contribution of effective quantum gravity to the high energy scattering in the framework of modified perturbation theory and one loop approximation

The asymptotic behavior of the scattering amplitude for two scalar particles at high energies with fixed momentum transfers is studied. The study is done within the effective theory of quantum gravity based on quasi-potential equation. By using the modified perturbation theory, a systematic method is developed to find the leading eikonal scattering amplitudes together with corrections to them in the one-loop gravitational approximation. The relation is established and discussed between the solutions obtained by means of the operator and functional approaches applied to quasi-potential equation. The first non-leading corrections to the leading eikonal amplitude are found.

Higgs inflation and the refined dS conjecture

The refined de Sitter derivative conjecture provides constraints to potentials that are low energy effective theories of quantum gravity. It can give direct bounds on inflationary scenarios and determine whether the theory is in the Landscape or the Swampland. We consider the ‘Higgs inflation’ scenario taking the refined de Sitter derivative conjecture into account. Obtaining the critical lines for the potential, we find a conjecture parameter space in which the ‘Higgs inflation’ is to be in the Landscape. Comparing with the model independent observational bounds from recent data we find that the observational bounds represent the Higgs inflation can be in the Landscape.

R2 inflation to probe non-perturbative quantum gravity

It is natural to expect a consistent inflationary model of the very early Universe to be an effective theory of quantum gravity, at least at energies much less than the Planck one. For the moment, R + R2, or shortly R2, inflation is the most successful in accounting for the latest CMB data from the PLANCK satellite and other experiments. Moreover, recently it was shown to be ultra-violet (UV) complete via an embedding into an analytic infinite derivative (AID) non-local gravity. In this paper, we derive a most general theory of gravity that contributes to perturbed linear equations of motion around maximally symmetric space-times. We show that such a theory is quadratic in the Ricci scalar and the Weyl tensor with AID operators along with the Einstein-Hilbert term and possibly a cosmological constant. We explicitly demonstrate that introduction of the Ricci tensor squared term is redundant. Working in this quadratic AID gravity framework without a cosmological term we prove that for a specified class of space homogeneous space-times, a space of solutions to the equations of motion is identical to the space of backgrounds in a local R2 model. We further compute the full second order perturbed action around any background belonging to that class. We proceed by extracting the key inflationary parameters of our model such as a spectral index (ns), a tensor-to-scalar ratio (r) and a tensor tilt (nt). It appears that ns remains the same as in the local R2 inflation in the leading slow-roll approximation, while r and nt get modified due to modification of the tensor power spectrum. This class of models allows for any value of r < 0.07 with a modified consistency relation which can be fixed by future observations of primordial B-modes of the CMB polarization. This makes the UV complete R2 gravity a natural target for future CMB probes.

Gravitational effective action at second order in curvature and gravitational waves

We consider the full effective theory for quantum gravity at second order in curvature including non-local terms. We show that the theory contains two new degrees of freedom beyond the massless graviton: namely a massive spin-2 ghost and a massive scalar field. Furthermore, we show that it is impossible to fine-tune the parameters of the effective action to eliminate completely the classical spin-2 ghost because of the non-local terms in the effective action. Being a classical field, it is not clear anyway that this ghost is problematic. It simply implies a repulsive contribution to Newton’s potential. We then consider how to extract the parameters of the effective action and show that it is possible to measure, at least in principle, the parameters of the local terms independently of each other using a combination of observations of gravitational waves and measurements performed by pendulum type experiments searching for deviations of Newton’s potential.

Do we have unitary and (super)renormalizable quantum gravity below the Planck scale?

We explore how the stability of metric perturbations in higher derivative theories of gravity depends on the energy scale of initial seeds of such perturbations and on a typical energy scale of the gravitational vacuum background. It is shown that, at least in the cases of specific cosmological backgrounds, that the unphysical massive ghost which is present in the spectrum of such theories is not growing up as a physical excitation and remains in the vacuum state, until the initial frequency of the perturbation is close to the Planck order of magnitude. In this situation the existing versions of renormalizable and superrenormalizable theories can be seen as very satisfactory effective theories of Quantum Gravity below the Planck scale.

EFFECTIVE THEORY FOR QUANTUM GRAVITY

In this paper, we discuss an effective theory for quantum gravity and discuss the bounds on the parameters of this effective action. In particular, we show that measurement in pulsars binary systems are unlikely to improve the bounds on the coefficients of the R2 and RμνRμν terms obtained from probes of Newton's potential performed on Earth. Furthermore, we argue that if the coefficients of these terms are induced by quantum gravity, they should be at most of order unity since R2 and RμνRμν are dimension four operators. The same applies to the nonminimal coupling of the Higgs boson to the Ricci scalar.

Myers–Pospelov model as an ensemble of Pais–Uhlenbeck oscillators: unitarity and Lorentz invariance violation

We study a generalization of a Pais-Uhlenbeck oscillator for fermionic variables. Next, we consider an ensemble of these oscillators and we identify a particular case of the Myers-Pospelov model which is relevant for effective theories of quantum gravity. Finally, by taking the advantage of this connection, we analyze, for this model, the unitarity at one loop order in the low energy regime where no ghost states can be created on-shell. This energy regime is the relevant one when we consider the Myers-Pospelov model as a true effective theory coming from new space-time structure.

Interacting scalar fields in the context of effective quantum gravity

A four-dimensional scalar field theory with quartic and of higher-power interactions suffers the triviality issue at the quantum level. This is due to coupling constants that, contrary to the physical expectations, seem to grow without a bound with energy. Since this problem concerns the high- energy domain, interaction with a quantum gravitational field may provide a natural solution to it. In this paper we address this problem considering a scalar field theory with a general analytic potential having ${\mathbb{Z}}_{2}$ symmetry and interacting with a quantum gravitational field. The dynamics of the latter is governed by the cosmological constant and the Einstein-Hilbert term, both being the lowest and next-to-lowest terms of the effective theory of quantum gravity. Using the Vilkovisky-DeWitt method we calculate the one-loop correction to the scalar field effective action. We also derive the gauge-independent one-loop beta functions for all the scalar field couplings in the minimal subtraction scheme. We find that the leading gravitational corrections act in the direction of asymptotic freedom. Moreover, assuming both the Newton and cosmological constants have nonzero fixed point values, we find asymptotically free Halpern-Huang potentials.

NONCOMMUTATIVE BLACK HOLES, THE FINAL APPEAL TO QUANTUM GRAVITY: A REVIEW

We present the state of the art regarding the relation between the physics of Quantum Black Holes and Noncommutative Geometry. We start with a review of models proposed in the literature for describing deformations of General Relativity in the presence of noncommutativity, seen as an effective theory of Quantum Gravity. We study the resulting metrics, proposed to replace or at least to improve the conventional black hole solutions of Einstein's equation. In particular, we analyze noncommutative-inspired solutions obtained in terms of quasiclassical noncommutative coordinates: indeed because of their surprising new features, these solutions enable us to circumvent long standing problems with Quantum Field Theory in Curved Space and to cure the singular behavior of gravity at the centers of black holes. As a consequence, for the first time, we get a complete description of what we may call the black hole SCRAM, the shut down of the emission of thermal radiation from the black hole: in place of the conventional scenario of runaway evaporation in the Planck phase, we find a zero temperature final state, a stable black hole remnant, whose size and mass are determined uniquely in terms of the noncommutative parameter θ. This result turns out to be of vital importance for the physics of the forthcoming experiments at the LHC, where mini black hole production is foreseen in extreme energy hadron collisions. Because of this, we devote the final part of this review to higher-dimensional solutions and their phenomenological implications for TeV Gravity.

Observables in effective gravity

We address the construction and interpretation of diffeomorphism-invariant observables in a low-energy effective theory of quantum gravity. The observables we consider are constructed as integrals over the space of coordinates, in analogy to the construction of gauge-invariant observables in Yang-Mills theory via traces. As such, they are explicitly nonlocal. Nevertheless we describe how, in suitable quantum states and in a suitable limit, the familiar physics of local quantum field theory can be recovered from appropriate such observables, which we term ``pseudolocal.'' We consider measurement of pseudolocal observables, and describe how such measurements are limited by both quantum effects and gravitational interactions. These limitations support suggestions that theories of quantum gravity associated with finite regions of spacetime contain far fewer degrees of freedom than do local field theories.

Unrenormalizable theories can be predictive

Unrenormalizable theories contain infinitely many free parameters. Considering these theories in terms of the Wilsonian renormalization group (RG), we suggest a method for removing this large ambiguity. Our basic assumption is the existence of a maximal ultraviolet cutoff in a cutoff theory, and we require that the theory be so fine tuned as to reach the maximal cutoff. The theory so obtained behaves as a local continuum theory to the shortest distance. In concrete examples of the scalar theory we find that at least in a certain approximation to the Wilsonian RG, this requirement enables us to make unique predictions in the infrared regime in terms of a finite number of independent parameters. Therefore, this method might provide a way for calculating quantum corrections in a low-energy effective theory of quantum gravity.

Manifestations of quantum gravity in scalar QED phenomena.

Quantum gravitational corrections to the effective potential, at one-loop level and in the leading-log approximation, for scalar quantum electrodynamics with higher-derivative gravity ---which is taken as an effective theory for quantum gravity (QG)--- are calculated. We point out the appearence of relevant phenomena caused by quantum gravity, like dimensional transmutation, QG-driven instabilities of the potential, QG corrrections to scalar-to-vector mass ratios, and curvature-induced phase transitions, whose existence is shown by means of analytical and numerical study.

CONFORMAL FACTOR DYNAMICS IN THE 1/N EXPANSION

We suggest to consider conformal factor dynamics as applying to composite bound states, in the framework of the 1/N expansion. In this way, a new model of effective theory for quantum gravity is obtained. The renormalization group (RG) analysis of this model provides a framework to solve the cosmological constant problem, since the value of this constant turns out to be suppressed, as a result of the RG contributions. The effective potential for the conformal factor is also found.

Asymptotic regimes in quantum gravity at large distances and running Newtonian and cosmological constants

We consider a multiplicatively renormalizable higher-derivative scalar theory which is used as an effective theory for quantum gravity at large distances (infrared phase of quantum gravity). The asymptotic regimes (in particular, the asymptotically free infrared regime) for the coupling constants---specifically the Newtonian and the cosmological constant---are obtained. The running of the Newton and cosmological constants in the infrared asymptotically free regime may be relevant for solving the cosmological constant problem and for estimating the leading-log corrections to the static gravitational potential.