Curvature Coupling Research Articles

Fate of electroweak vacuum during preheating

Our electroweak vacuum may be metastable in light of the current experimental data of the Higgs/top quark mass. If this is really the case, high-scale inflation models require a stabilization mechanism of our vacuum during inflation. A possible candidate is the Higgs-inflaton/-curvature coupling because it induces an additional mass term to the Higgs during the slow roll regime. However, after inflation, the additional mass term oscillates, and it can destabilize our electroweak vacuum via production of large Higgs fluctuations during the inflaton oscillation era. In this paper, we study whether or not the Higgs-inflaton/-curvature coupling can save our vacuum by properly taking account of Higgs production during the preheating stage. We put upper bounds on the Higgs-inflaton and -curvature couplings, and discuss possible dynamics that might relax them.

Isogeometric Reissner‐Mindlin shell analysis ‐ employing different control meshes for displacements and rotations

AbstractThe main purpose of this paper is the development and implementation of a method for the reduction of the so‐called locking effect in the isogeometric Reissner‐Mindlin shell formulation. In [1] an isogeometric Reissner‐Mindlin shell formulation with an exact interpolation of the director vector based on continuum mechanics was introduced. The numerical examples showed that the accuracy and efficiency increased. However, there are only few effective concepts for the prevention of locking effects for low polynomial degrees. In the work of Beirão da Veiga [2], shear locking is prevented for a Reissner‐Mindlin plate formulation by using suitable solution spaces. Here, the method is extended to the Reissner‐Mindlin shell formulation. Different control meshes are used for displacements and rotations. Furthermore, the basis functions in the direction of the relevant rotation are one degree less than the ones which are chosen for the displacements. That leads to control meshes with different number and location of the control points. The aim is to avoid shear locking due to the coupling of shear strains and curvature since the compatibility requirement for pure bending is then fulfilled. The accuracy and efficiency of this method are investigated for different examples. In addition, the results are compared to the analytical solutions. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Cosmic acceleration from matter–curvature coupling

We consider f(R,T) modified theory of gravity in which, in general, the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar and the trace of the energy-momentum tensor. We indicate that in this type of the theory, the coupling energy-momentum tensor is~not conserved. However, we mainly focus on a particular model that matter is minimally coupled to the geometry in the metric formalism and wherein, its coupling energy--momentum tensor is also conserved. We obtain the corresponding Raychaudhuri dynamical equation that presents the evolution of the kinematic quantities. Then for the chosen model, we derive the behavior of the deceleration parameter, and show that the coupling term can lead to an acceleration phase after the matter dominated phase. On the other hand, the curvature of the universe corresponds with the deviation from parallelism in the geodesic motion. Thus, we also scrutinize the motion of the free test particles on their geodesics, and derive the geodesic deviation equation in this modified theory to study the accelerating universe within the spatially flat FLRW background. Actually, this equation gives the relative accelerations of adjacent particles as a measurable physical quantity, and provides an elegant tool to investigate the timelike and the null structures of spacetime geometries. Then, through the null deviation vector, we find the observer area-distance as a function of the redshift for the chosen model, and compare the results with the corresponding results obtained in the literature.

Anisotropic cubic curvature couplings

To complement recent work on tests of spacetime symmetry in gravity, cubic curvature couplings are studied using an effective field theory description of spacetime-symmetry breaking. The associated mass dimension 8 coefficients for Lorentz violation studied do not result in any linearized gravity modifications and instead are revealed in the first nonlinear terms in an expansion of spacetime around a flat background. We consider effects on gravitational radiation through the energy loss of a binary system and we study two-body orbital perturbations using the post-Newtonian metric. Some effects depend on the internal structure of the source and test bodies, thereby breaking the Weak Equivalence Principle for self-gravitating bodies. These coefficients can be measured in solar-system tests, while binary-pulsar systems and short-range gravity tests are particularly sensitive.

Combined Search for Lorentz Violation in Short-Range Gravity.

Short-range experiments testing the gravitational inverse-square law at the submillimeter scale offer uniquely sensitive probes of Lorentz invariance. A combined analysis of results from the short-range gravity experiments HUST-2015, HUST-2011, IU-2012, and IU-2002 permits the first independent measurements of the 14 nonrelativistic coefficients for Lorentz violation in the pure-gravity sector at the level of 10^{-9} m^{2}, improving by an order of magnitude the sensitivity to numerous types of Lorentz violation involving quadratic curvature derivatives and curvature couplings.

Coriolis effect and spin Hall effect of light in an inhomogeneous chiral medium.

We theoretically investigate the spin Hall effect of spinning light in an inhomogeneous chiral medium. The Hamiltonian equations of the photon are analytically obtained within eikonal approximation in the noninertial orthogonal frame. Besides the usual spin curvature coupling, the chiral parameter enters the Hamiltonian as a spin-torsion-like interaction. We reveal that both terms have parallel geometric origins as the Coriolis terms of Maxwell's equations in nontrivial frames.

Entropy functionals andc-theorems from the second law

We show that for a general four derivative theory of gravity, only the holographic entanglement entropy functionals obey the second law at linearized order in perturbations. We also derive bounds on the higher curvature couplings in several examples, demanding the validity of the second law for higher order perturbations. For the five dimensional Gauss-Bonnet theory in the context of AdS/CFT, the bound arising from black branes coincides with there being no sound channel instability close to the horizon. Repeating the analysis for topological black holes, the bound coincides with the tensor channel causality constraint (which is responsible for the viscosity bound). Furthermore, we show how to recover the holographic c-theorems in higher curvature theories from similar considerations based on the Raychaudhuri equation.

Monolithic fiber end cap collimator for high-power free-space fiber-fiber coupling.

In this paper, we present the design, construction, and testing of a monolithic fiber end cap collimator for high-power free-space fiber-fiber coupling applications. The collimator is based on a large-sized fiber end cap and a spherical lens design on the output facet. Values of the spot size and working distance are theoretically analyzed based on Gaussian approximation and ABCD transmission matrix. The free-space fiber-fiber coupling process is also analyzed for different lens curvature radii and coupling distances. In the experiment, a collimated laser beam is obtained with Rayleigh length of about 400mm. A high-power laser with 1.1kW output is tested on the end cap collimator, which only heats up by 7°C at the output facet without active cooling. Free-space fiber-fiber coupling between two 20/400μm fibers is achieved based on these collimators, with measured coupling loss lower than 0.3dB.

RG flow and thermodynamics of causal horizons in higher-derivative AdS gravity

In arXiv:1508.01343 [hep-th], one of the authors proposed that in AdS/CFT the gravity dual of the boundary $c$-theorem is the second law of thermodynamics satisfied by causal horizons in AdS and this was verified for Einstein gravity in the bulk. In this paper we verify this for higher derivative theories. We pick up theories for which an entropy expression satisfying the second law exists and show that the entropy density evaluated on the causal horizon in a RG flow geometry is a holographic c-function. We also prove that given a theory of gravity described by a local covariant action in the bulk a sufficient condition to ensure holographic c-theorem is that the second law of causal horizon thermodynamics be satisfied by the theory. This allows us to explicitly construct holographic c-function in a theory where there is curvature coupling between gravity and matter and standard null energy condition cannot be defined although second law is known to hold. Based on the duality between c-theorem and the second law of causal horizon thermodynamics proposed in arXiv:1508.01343 [hep-th] and the supporting calculations of this paper we conjecture that every Unitary higher derivative theory of gravity in AdS satisfies the second law of causal horizon thermodynamics. If this is not true then c-theorem will be violated in a unitary Lorentz invariant field theory.

Detection of gravitational frame dragging using orbiting qubits

In this paper we propose information theoretic and interferometric techniques to detect the effect of gravitational frame dragging on orbiting qubits. In particular, we consider the Kerr spacetime geometry and spin- qubits moving in equatorial circular orbits. We ignore the order effects due to spin–curvature coupling, which allows us to consider the motion of the spin- particles as Kerr geometry geodesics. We derive analytical expressions for the infinitesimal Wigner rotation and numerical results for their integration across the length of the particle’s trajectory. To this end, we consider the bounds on the finite Wigner rotation imposed by Penrose’s cosmic censorship hypothesis. Finally we propose how the Wigner rotation strictly due to frame dragging could be observed using interferometry and other quantum metrology techniques.

Modular Nuclearity: A Generally Covariant Perspective

A quantum field theory in its algebraic description may admit many irregular states. So far, selection criteria to distinguish physically reasonable states have been restricted to free fields (Hadamard condition) or to flat spacetimes (e.g., Buchholz-Wichmann nuclearity). We propose instead to use a modular ℓp -condition, which is an extension of a strengthened modular nuclearity condition to generally covariant theories. The modular nuclearity condition was previously introduced in Minkowski space, where it played an important role in constructive two dimensional algebraic QFT’s. We show that our generally covariant extension of this condition makes sense for a vast range of theories, and that it behaves well under causal propagation and taking mixtures. In addition we show that our modular ℓp -condition holds for every quasi-free Hadamard state of a free scalar quantum field (regardless of mass or scalar curvature coupling). However, our condition is not equivalent to the Hadamard condition.

Search for Lorentz invariance violation by tests of the gravitational inverse square law at short ranges

We review the recent development on search for Lorentz invariance violation by tests of the gravitational inverse square law at short ranges. Inverse-square law tests usually use planar geometry to search for the non-Newtonian gravity, which are also well suited for exploration of local Lorentz invariance for spacetime-based gravitation. Recent studies of Lorentz invariance violation in pure gravity sector show that the general quadratic curvature coupling will lead to interesting new effects in short range experiments, resulting in the sidereal variations in the non-Newtonian force between two metal plates at short ranges. We show that the Lorentz invariance violation force between two finite flat plates is dominated by the edge effects, which adds an extra suppression factor. Nevertheless, the best current constraints of the Lorentz invariance violating coefficients are determined at a level of 10-8 m2.

Vacuum currents in braneworlds on AdS bulk with compact dimensions

The two-point function and VEV of the current density are investigated for a massive charged scalar field with arbitrary curvature coupling in the geometry of a brane on background of AdS spacetime with partial toroidal compactification.The presence of a gauge field flux enclosed by compact dimensions is assumed.On the brane the field obeys Robin boundary condition and along compact dimensions periodicity conditions with general phases are imposed.There is a range in the space of values for the coefficient in the boundary condition where Poincare vacuum is unstable.This range depends on the brane location.In models with compact dimensions the stability condition is less restrictive than for AdS bulk with trivial topology.Vacuum charge density and components of current along non-compact dimensions vanish. VEV of the current density along compact dimensions is a periodic function of the gauge field flux with a period equal to the flux quantum.It is decomposed into the boundary-free and brane-induced contributions.The asymptotic behavior of the latter is investigated near the brane, AdS boundary and horizon.In contrast to VEVs of the field squared and energy-momentum tensor, current density is finite on brane and vanishes for the special case of Dirichlet boundary condition.Both boundary-free and brane-induced contributions vanish on AdS boundary.Brane-induced contribution vanishes on the horizon and for points near the horizon the current is dominated by the boundary-free part.In the near-horizon limit, the latter is connected to the corresponding quantity for a massless field in the Minkowski bulk by a simple conformal relation.Depending on the value of the Robin coefficient, the presence of the brane can either increase or decrease the vacuum currents. Applications are given for a higher-dimensional version of the Randall-Sundrum 1-brane model

Buckling behavior under radial loading of orthotropic oval cylindrical shells with parabolically varying thickness

ABSTRACTIn this article, the framework of the Flügge's shell theory, the transfer matrix approach, and the Romberg integration method have been employed to investigate the buckling analysis of a radial loaded oval cylindrical shell with parabolically varying thickness along its circumference. Trigonometric functions are used to form the modal displacements of the shell and Fourier's approach is used to separate the variables. The mathematical analysis is formulated to overcome the difficulties related to mode coupling of variable curvature and thickness of the shell. Using the transfer matrix of the shell, the buckling equations of the shell are reduced to eight first-order differential equations in the circumferential coordinate and rewritten in a matrix form and solved numerically. The proposed model is adopted to get the critical buckling loads and the corresponding buckling deformations for the symmetrical and antisymmetrical modes of buckling. The influences of the shell geometry, orthotropic parameters, ovality parameter, and thickness ratio on the buckling parameters and the bending deformations are presented for different type-modes of buckling.

Comments on universal properties of entanglement entropy and bulk reconstruction

Entanglement entropy of holographic CFTs is expected to play a crucial role in the reconstruction of semiclassical bulk gravity. We consider the entanglement entropy of spherical regions of vacuum, which is known to contain universal contributions. After perturbing the CFT with a relevant scalar operator, also the first order change of this quantity gives a universal term which only depends on a discrete set of basic CFT parameters. We show that in gravity this statement corresponds to the uniqueness of the ghost-free graviton propagator on an AdS background geometry. While the gravitational dynamics in this context contains little information about the structure of the bulk theory, there is a discrete set of dimensionless parameters of the theory which determines the entanglement entropy. We argue that for every (not necessarily holographic) CFT, any reasonable gravity model can be used to compute this particular entanglement entropy. We elucidate how this statement is consistent with AdS/CFT and also give various generalizations. On the one hand this illustrates the remarkable usefulness of geometric concepts for understanding entanglement in general CFTs. On the other hand, it provides hints as to what entanglement data can be expected to provide enough information to distinguish, e.g., bulk theories with different higher curvature couplings.

Maximization of the fundamental frequency of plates and cylinders

This work deals with the maximization of the fundamental frequency of laminated plates and cylinders by finding the optimal stacking sequence for symmetric and balanced laminates with neglectable bending–twisting and torsion–curvature couplings are considered. Instead of using the angle at each ply the so-called lamination parameters are used as design variables. Results for the plate problem are compared to those using analytical expressions found in the literature. The cylinder problem is solved for a large number of thickness and radius-to-length ratio combinations. Values of the optimal stacking sequence are given considering the angle can take any value between 0° and 90° or the case when the angle can only take a discrete set of values.

Inside the Schwarzschild-Tangherlini black holes

The first-order semiclassical Einstein field equations are solved in the interior of the Schwarzschild-Tangherlini black holes. The source term is taken to be the stress-energy tensor of the quantized massive scalar field with arbitrary curvature coupling calculated within the framework of the Schwinger-DeWitt approximation. It is shown that for the minimal coupling the quantum effects tend to isotropize the interior of the black hole (which can be interpreted as an anisotropic collapsing universe) for D=4 and 5, whereas for D=6 and 7 the spacetime becomes more anisotropic. Similar behavior is observed for the conformal coupling with the reservation that for D=5 isotropization of the spacetime occurs during (approximately) the first 1/3 of the lifetime of the interior universe. On the other hand, we find that regardless of the dimension, the quantum perturbations initially strengthen the grow of curvature and its later behavior depends on the dimension and the coupling. It is shown that the Karlhede's scalar can still be used as a useful device for locating the horizon of the quantum-corrected black hole, as expected.

Casimir Effect in Hemisphere Capped Tubes

In this paper we investigate the vacuum densities for a massive scalar field with general curvature coupling in background of a (2+1)-dimensional spacetime corresponding to a cylindrical tube with a hemispherical cap. A complete set of mode functions is constructed and the positive-frequency Wightman function is evaluated for both the cylindrical and hemispherical subspaces. On the base of this, the vacuum expectation values of the field squared and energy-momentum tensor are investigated. The mean field squared and the normal stress are finite on the boundary separating two subspaces, whereas the energy density and the parallel stress diverge as the inverse power of the distance from the boundary. For a conformally coupled field, the vacuum energy density is negative on the cylindrical part of the space. On the hemisphere, it is negative near the top and positive close to the boundary. In the case of minimal coupling the energy density on the cup is negative. On the tube it is positive near the boundary and negative at large distances. Though the geometries of the subspaces are different, the Casimir pressures on the separate sides of the boundary are equal and the net Casimir force vanishes. The results obtained may be applied to capped carbon nanotubes described by an effective field theory in the long-wavelength approximation.

Regulation of Membrane-Shape Transitions Induced by I-BAR Domains

I-BAR proteins are well-known actin-cytoskeleton adaptors and have been observed to be involved in the formation of plasma membrane protrusions (filopodia). I-BAR proteins contain an all-helical, crescent-shaped IRSp53-MIM domain (IMD) dimer that is believed to be able to couple with a membrane shape. This coupling could involve the sensing and even the generation of negative plasma membrane curvature. Indeed, the in vitro studies have shown that IMDs can induce inward tubulation of liposomes. While N-BAR domains, which generate positive membrane curvature, have received a considerable amount of attention from both theory and experiments, the mechanisms of curvature coupling through IMDs are comparatively less studied and understood. Here we used a membrane-shape stability assay developed recently in our lab to quantitatively characterize IMD-induced membrane-shape transitions. We determined a membrane-shape stability diagram for IMDs that reveals how membrane tension and protein density can comodulate the generation of IMD-induced membrane protrusions. From comparison to analytical theory, we determine three key parameters that characterize the curvature coupling of IMD. We find that the curvature generation capacity of IMDs is significantly stronger compared to that of endophilin, an N-BAR protein known to be involved in plasma membrane shape transitions. Contrary to N-BAR domains, where amphipathic helix insertion is known to promote its membrane curvature generation, for IMDs we find that amphipathic helices inhibit membrane shape transitions, consistent with the inverse curvature that IMDs generate. Importantly, in both of these types of BAR domains, electrostatic interactions affect membrane-binding capacity, but do not appear to affect the curvature generation capacity of the protein. These two types of BAR domain proteins show qualitatively similar membrane shape stability diagrams, suggesting an underlying ubiquitous mechanism by which peripheral proteins regulate membrane curvature.

Traversable wormholes and classical scalar fields

I prove that general relativity admits no asymptotically well-behaved static spherically symmetric traversable wormholes supported by classical scalar fields and nonexotic matter. The theorem holds for all values of the scalar field curvature coupling parameter $\ensuremath{\xi}$, even though fields with $\ensuremath{\xi}>0$ are capable of violating the average null energy condition. Good asymptotic behavior (the effective Newton's constant being positive and finite at both ends of the wormhole) can only be achieved by introducing additional exotic matter, which must itself violate the null energy condition over some region of nonzero volume. These results are insensitive to the number of scalar fields, the form of their potentials, and the coupling between the fields and the additional matter.