Gravitational Corrections Research Articles

Gauge independent quantum gravitational corrections to Maxwell\u2019s equation

We consider quantum gravitational corrections to Maxwell’s equations on flat space background. Although the vacuum polarization is highly gauge dependent, we explicitly show that this gauge dependence is canceled by contributions from the source which disturbs the effective field and the observer who measures it. Our final result is a gauge independent, real and causal effective field equation that can be used in the same way as the classical Maxwell equation.

Covariant effective action for scalar-tensor theories of gravity

We develop the calculation of the divergent part of one-loop covariant effective action for scalar fields minimally and non-minimally coupled to gravity using the generalized Schwinger-DeWitt technique. We derive the field-space metric using Vilkovisky's prescription and obtain new terms in the one-loop corrections which are absent in past literature with trivial choices of field-space metric. We further calculate the covariant versions of past results, obtained using the standard approach, by applying Barvinsky and Vilkovisky's extension to the ordinary Schwinger-DeWitt approach. For completeness, we study the one-loop gravitational corrections for a dilaton-extended two-field Starobinsky model and compare with known results.

Exactly solvable vacuum decays with gravity

Using a new approach to the analysis of false vacuum decay based on the so-called tunneling potential, we develop a general method to find scalar potentials with a false vacuum with exactly solvable decay at the semi-classical level, including gravitational corrections. We examine in particular the decays of de Sitter vacua providing concrete examples that allow to explore analytically the transition between the Coleman-De Luccia and Hawking-Moss regimes.

Oscillations in the extreme mass-ratio inspiral gravitational wave phase correction as a probe of a reflective boundary of the central black hole

We discuss the energy loss due to gravitational radiation of binaries composed of exotic objects whose horizon boundary conditions are replaced with reflective ones. Our focus is on the extreme mass-ratio inspirals, in which the central heavier black hole is replaced with an exotic compact object. We show, in this case, a modulation of the energy loss rate depending on the evolving orbital frequency occurs and leads to two different types of modifications to the gravitational wave phase evolution; the oscillating part directly corresponding to the modulation in the energy flux, and the non-oscillating part coming from the quadratic order in the modulation. This modification can be sufficiently large to detect with future space-borne detectors.

High energy scattering in perturbative quantum gravity at next-to-leading power

We consider the relativistic scattering of unequal-mass scalar particles through graviton exchange in the small-angle high-energy regime. We show the self-consistency of expansion around the eikonal limit and compute the scattering amplitude up to the next-to-leading power correction of the light particle energy, including gravitational effects of the same order. The first power correction is suppressed by a single power of the ratio of momentum transfer to the energy of the light particle in the rest frame of the heavy particle, independent of the heavy particle mass. We find that only gravitational corrections contribute to the exponentiated phase in impact parameter space in four dimensions. For large enough heavy-particle mass, the saddle point for the impact parameter is modified compared to the leading order by a multiple of the Schwarzschild radius determined by the mass of the heavy particle, independent of the energy of the light particle.

Two dimensional nearly de Sitter gravity

We study some aspects of the de Sitter version of Jackiw-Teitelboim gravity. Though we do not have propagating gravitons, we have a boundary mode when we compute observables with a fixed dilaton and metric at the boundary. We compute the no-boundary wavefunctions and probability measures to all orders in perturbation theory. We also discuss contributions from different topologies, borrowing recent results by Saad, Shenker and Stanford. We discuss how the boundary mode leads to gravitational corrections to cosmological observables when we add matter. Finally, starting from a four dimensional gravity theory with a positive cosmological constant, we consider a nearly extremal black hole and argue that some observables are dominated by the two dimensional nearly de Sitter gravity dynamics.

Comparison of Gravitational and Light Frequency Shifts in Rubidium Atomic Clock

The article presents the results of an experimental study of the external magnetic field orientation and magnitude influence on the rubidium atomic clock, simulating the influence of the geomagnetic field on the onboard rubidium atomic clock of navigation satellites. The tensor component value of the atomic clock frequency light shift on the rubidium cell was obtained, and this value was ~2 Hz. The comparability of the relative light shift (~10−9) and the regular gravitational correction (4×10−10) to the frequency of the rubidium atomic clock was shown. The experimental results to determine the orientational shift influence on the rubidium atomic clock frequency were presented. A significant effect on the relative frequency instability of a rubidium atomic clock at a level of 10−12(10−13) for rotating external magnetic field amplitudes of 1.5 A/m and 3 A/m was demonstrated. This magnitude corresponds to the geomagnetic field in the orbit of navigation satellites. The necessity of taking into account various factors (satellite orbit parameters and atomic clock characteristics) is substantiated for correct comparison of corrections to the rubidium onboard atomic clock frequency associated with the Earth’s gravitational field action and the satellite orientation in the geomagnetic field.

Graviton loop contribution to Higgs potential in gauge–Higgs unification

Abstract We study the two-loop finiteness of an effective potential for a Higgs boson that is the fifth component of a gauge field in a $U(1)$ gauge theory coupled to quantum gravity on the five-dimensional space-time $M^4\times S^1$. There are two types of diagrams including quantum gravitational corrections. We find that only one type of diagram contributes to the effective potential for the Higgs boson, and its magnitude is finite.

Probing the Planck scale: the modification of the time evolution operator due to the quantum structure of spacetime

The propagator which evolves the wave-function in non-relativistic quantum mechanics, can be expressed as a matrix element of a time evolution operator: i.e. GNR(x) = 〈x2|UNR(t)|x1〉 in terms of the orthonormal eigenkets |x〉 of the position operator. In quantum field theory, it is not possible to define a conceptually useful single-particle position operator or its eigenkets. It is also not possible to interpret the relativistic (Feynman) propagator GR(x) as evolving any kind of single-particle wave-functions. In spite of all these, it is indeed possible to express the propagator of a free spinless particle, in quantum field theory, as a matrix element 〈x2|UR(t)|x1〉 for a suitably defined time evolution operator and (non-orthonormal) kets |x〉 labeled by spatial coordinates. At mesoscopic scales, which are close but not too close to Planck scale, one can incorporate quantum gravitational corrections to the propagator by introducing a zero-point-length. It turns out that even this quantum-gravity-corrected propagator can be expressed as a matrix element 〈x2|UQG(t)|x1〉. I describe these results and explore several consequences. It turns out that the evolution operator UQG(t) becomes non-unitary for sub-Planckian time intervals while remaining unitary for time interval is larger than Planck time. The results can be generalized to any ultrastatic curved spacetime.

Quantum corrected equations of motion in the interior and exterior Schwarzschild spacetimes

In this paper we derive the leading quantum gravitational corrections to the geodesics and the equations of motion for a scalar field in the spacetime containing a constant density star. It is shown that these corrections can be calculated in quantum gravity reliably and in a model independent way. Furthermore, we find that quantum gravity gives rise to an additional redshift that results from the gradient instead of the amplitude of the density profile.

Lorentz invariance violations in the interplay of quantum gravity with matter

We explore the interplay of matter with quantum gravity with a preferred frame to highlight that the matter sector cannot be protected from the symmetry-breaking effects in the gravitational sector. Focusing on Abelian gauge fields, we show that quantum gravitational radiative corrections induce Lorentz-invariance-violating couplings for the Abelian gauge field. In particular, we discuss how such a mechanism could result in the possibility to translate observational constraints on Lorentz violation in the matter sector into strong constraints on the Lorentz-violating gravitational couplings.

Singularities in quantum corrected space-times

In this paper we consider a static and regular fluid generating a locally spherically symmetric and time-independent space-time and calculate the leading quantum corrections to the metric to first order in curvature. Starting from a singularity free classical solution of general relativity, we show that singularities can be introduced in the curvature invariants by quantum gravitational corrections calculated using an effective field theory approach to quantum gravity. We identify non-trivial conditions that ensure that curvature invariants remain singularity free to leading order in the curvature expansion of the effective action.

The stabilizing effect of gravity made simple

A new approach to vacuum decay in quantum field theory, based on a simple variational formulation in field space using a tunneling potential, is ideally suited to study the effects of gravity on such decays. The method allows to prove in new and simple ways many results, among others, that gravitational corrections tend to make Minkowski or Anti de Sitter false vacua more stable semiclassically or that higher barriers increase vacuum lifetime. The approach also offers a very clean picture of gravitational quenching of vacuum decay and its parametric dependence on the features of a potential and allows to study the BPS domain-walls between vacua in critical cases. Special attention is devoted to supersymmetric potentials and to the discussion of near-critical vacuum decays, for which it is shown how the new method can be usefully applied beyond the thin-wall approximation.

Vacuum decay in the Standard Model: analytical results with running and gravity

A tunneling bounce driving the decay of a metastable vacuum must respect an integral constraint dictated by simple scaling arguments that is very useful to determine key properties of the bounce. After illustrating how this works in a simple toy model, the Standard Model Higgs potential is considered, including quartic coupling running and gravitational corrections as sources of scale invariance breaking. This approach clarifies the existence of the bounce and leads to simple and accurate analytical results in an expansion in the breaking parameters. Using the so-called tunneling-potential approach (generalized for nonminimal coupling to gravity) the integral constraint and the tunneling action are extended to second order in perturbations.

Covariant quantum corrections to a scalar field model inspired by nonminimal natural inflation

We calculate the covariant one-loop quantum gravitational effective action for a scalar field model inspired by the recently proposed nonminimal natural inflation model. Our calculation is perturbative, in the sense that the effective action is evaluated in orders of background field, around a Minkowski background. The effective potential has been evaluated taking into account the finite corrections. An order-of-magnitude estimate of the one-loop corrections reveals that gravitational and non-gravitational corrections have same or comparable magnitudes.

Cosmological perfect fluids in higher-order gravity

We prove that in Robertson-Walker space-times (and in generalized Robertson-Walker spacetimes of dimension greater than 3 with divergence-free Weyl tensor) all higher-order gravitational corrections of the Hilbert-Einstein Lagrangian density $F(R,\square R, ... , \square^k R)$ have the form of perfect fluids in the field equations. This statement definitively allows to deal with dark energy fluids as curvature effects.

Theorem on vanishing contributions to sin2θW and the intermediate mass scale in grand unified theories with trinification symmetry

We prove that the values of the electroweak mixing angle $\sin^2\theta_W$ and intermediate mass scale $M_I$ have vanishing contributions due to one-loop, two-loop and gravitational corrections in Grand Unified Theories which accommodate an intermediate trinification symmetry ($G_{333D}$) invoked with spontaneous D-parity mechanism operative at mass scale greater than $M_I$. The proof of theorem is robust and we verify the results numerically using supersymmetric as well as non-supersymmetric version of $E_6$-GUT.

Anomalous anomalies from virtual black holes

We investigate gravitational UV/IR mixing models that predict a breakdown of low energy effective field theory, from loop-level, nonlocal gravitational corrections to particle processes. We determine how the choice of IR cutoff in these theories alters predictions for lepton magnetic moments. Using Brookhaven E821 muon magnetic moment data, we exclude models of UV/IR mixing with an IR cutoff set by a spherical volume enclosing the experiment. On the other hand, an IR cutoff defined by the simply connected spatial volume containing the trajectories of the muons implies a correction to the muon magnetic moment which may have already been observed.

Cosmology of Bianchi type-I metric using renormalization group approach for quantum gravity

We study the anisotropic Bianchi type-I cosmological model at late times, taking into account quantum gravitational corrections in the formalism of the exact renormalization group flow of the effective average action for gravity. The cosmological evolution equations are derived by including the scale dependence of Newton’s constant G and cosmological constant . We have considered the solutions of the flow equations for G and at next to leading order in the infrared cutoff scale. Using these scale dependent G and in Einstein equations for the Bianchi-I model, we obtain the scale factors in different directions. It is shown that the scale factors eventually evolve into FLRW universe for known matter like radiation. However, for dust and stiff matter we find that the universe need not evolve to the FLRW cosmology in general, but can also show Kasner type behaviour.

Quantum cosmology and the inflationary spectra from a nonminimally coupled inflaton

We calculate the quantum gravitational corrections to the Mukhanov-Sasaki equation obtained by the canonical quantization of the inflaton-gravity system. Our approach, which is based on the Born-Oppenheimer decomposition of the resulting Wheeler-DeWitt equation, was previously applied to a minimally coupled inflaton. In this article we examine the case of a non minimally coupled inflaton and, in particular, the induced gravity case is also discussed. Finally, the equation governing the quantum evolution of the inflationary perturbations is derived on a de Sitter background. Moreover the problem of the introduction of time is addressed and a generalized method, with respect to that used for the minimal coupling case, is illustrated. Such a generalized method can be applied to the universe wave function when, through the Born-Oppenheimer factorization, we decompose it into a part which contains the minisuperspace degrees of freedom and another which describes the perturbations.