The structure of f ( R )-brane model

Recently, a family of interesting analytical brane solutions were found in f ( R ) gravity with f(R)=R+αR2 in Bazeia et al. (Phys Lett B 729:127 2014 ). In these solutions, the inner brane structure can be turned on by tuning the value of the parameter α . In this paper, we investigate how the parameter α affects the localization and the quasilocalization of the tensorial gravitons around these solutions. It is found that, in a range of α , despite the brane having an inner structure, there is no graviton resonance. However, in some other regions of the parameter space, although the brane has no internal structure, the effective potential for the graviton Kaluza–Klein (KK) modes has a singular structure, and there exist a series of graviton resonant modes. The contribution of the massive graviton KK modes to Newton’s law of gravity is discussed briefly

Warped brane worlds in critical gravity

We investigate the brane models in arbitrary dimensional critical gravity presented in Lu and Pope (Phys Rev Lett 106:181302, 2011 ). For the models of the thin branes with codimension one, the Gibbons–Hawking surface term and the junction conditions are derived, with which the analytical solutions for the flat, AdS, and dS branes are obtained at the critical point of the critical gravity. It is found that all these branes are embedded in an AdS n spacetime, but, in general, the effective cosmological constant Λ of the AdS n spacetime is not equal to the naked one Λ0 in the critical gravity, which can be positive, zero, and negative. Another interesting result is that the brane tension can also be positive, zero, or negative, depending on the symmetry of the thin brane and the values of the parameters of the theory, which is very different from the case in general relativity. It is shown that the mass hierarchy problem can be solved in the braneworld model in the higher-derivative critical gravity. We also study the thick brane model and find analytical and numerical solutions of the flat, AdS, and dS branes. It is found that some branes will have inner structure when some parameters of the theory are larger than their critical values, which may result in resonant KK modes for some bulk matter fields. The flat branes with positive energy density and AdS branes with negative energy density are embedded in an n -dimensional AdS spacetime, while the dS branes with positive energy density are embedded in an n -dimensional Minkowski one

Brane worlds in gravity with auxiliary fields

Recently, Pani et al. explored a new theory of gravity by adding nondynamical fields, i.e., gravity with auxiliary fields (Phys Rev D 88:121502, 2013 ). In this gravity theory, higher-order derivatives of matter fields generically appear in the field equations. In this paper we extend this theory to any dimensions and discuss the thick braneworld model in five dimensions. Domain wall solutions are obtained numerically. The stability of the brane system under tensor perturbations is analyzed. We find that the system is stable under tensor perturbations and the gravity zero mode is localized on the brane. Therefore, the four-dimensional Newtonian potential can be realized on the brane

K -field kinks: stability, exact solutions and new features

We study a class of noncanonical real scalar field models in (1 + 1)-dimensional flat space-time. We first derive the general criterion for the classical linear stability of an arbitrary static soliton solution of these models. Then we construct first-order formalisms for some typical models and derive the corresponding kink solutions. The linear structures of these solutions are also qualitatively analyzed and compared with the canonical kink solutions

Black hole solution and strong gravitational lensing in Eddington-inspired Born–Infeld gravity

A new theory of gravity called Eddington-inspired Born–Infeld (EiBI) gravity was recently proposed by Bañados and Ferreira. This theory leads to some exciting new features, such as free of cosmological singularities. In this paper, we first obtain a charged EiBI black hole solution with a nonvanishing cosmological constant when the electromagnetic field is included in. Then based on it, we study the strong gravitational lensing by the asymptotic flat charged EiBI black hole. The strong deflection limit coefficients and observables are shown to closely depend on the additional coupling parameter κ in the EiBI gravity. It is found that, compared with the corresponding charged black hole in general relativity, the positive coupling parameter κ will shrink the black hole horizon and photon sphere. Moreover, the coupling parameter will decrease the angular position and relative magnitudes of the relativistic images, while increase the angular separation, which may shine new light on testing such gravity theory in near future by the astronomical instruments

Null Geodesics and Gravitational Lensing in a Nonsingular Spacetime

The null geodesics and gravitational lensing in a nonsingular spacetime are investigated. According to the nature of the null geodesics, the spacetime is divided into several cases. In the weak deflection limit, we find the influence of the nonsingularity parameter <math id="M1" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>q</mi></mrow></math> on the positions and magnifications of the images is negligible. In the strong deflection limit, the coefficients and observables for the gravitational lensing in a nonsingular black hole background and a weakly nonsingular spacetime are obtained. Comparing these results, we find that, in a weakly nonsingular spacetime, the relativistic images have smaller angular position and relative magnification but larger angular separation than those of a nonsingular black hole. These results might offer a way to probe the spacetime nonsingularity parameter and put a bound on it by the astronomical instruments in the near future

Localization and mass spectra of various matter fields on scalar-tensor brane

Recently, a new scalar-tensor braneworld model was presented in [Phys. Rev. D 86 (2012) 127502]. It not only solves the gauge hierarchy problem but also reproduces a correct Friedmann-like equation on the brane. In this new model, there are two different brane solutions, for which the mass spectra of gravity on the brane are the same. In this paper, we investigate localization and mass spectra of various bulk matter fields (i.e., scalar, vector, Kalb-Ramond, and fermion fields) on the brane. It is shown that the zero modes of all the matter fields can be localized on the positive tension brane under some conditions, and the mass spectra of each kind of bulk matter field for the two brane solutions are different except for some special cases, which implies that the two brane solutions are not physically equivalent. When the coupling constants between the dilaton and bulk matter fields take special values, the mass spectra for both solutions are the same, and the scalar and vector zero modes are localized on the negative tension brane, while the KR zero mode is still localized on the positive tension brane

Prediction of a missing higher charmonium around 4.26 GeV in J/ψ family

Inspired by the similarity between the mass gaps of the J/ψ and Υ families, the prediction of a missing higher charmonium with mass 4,263 MeV and very narrow width is made. In addition, the properties of two charmonium-like states, X(3940) and X(4160) , and charmonium ψ(4415) are discussed, where our calculation shows that X(3940) as ηc(3S) is established, while the explanation of X(4160) to be ηc(4S) is fully excluded and that ηc(4S) is typically a very narrow state. These predictions might be accessible at BESIII, Belle, and BelleII in near future

Simulating the charged charmoniumlike structure Zc(4025)

Inspired by the recent observation of the charged charmoniumlike structure Zc(4025) , we explore the Y(4260)→(D∗D¯∗)−π+ decay through the initial-single-pion-emission mechanism, where the D∗D¯∗→D∗D¯∗ interaction is studied by the ladder approximation, including the non-interacting case. Our calculation of the differential decay width for Y(4260)→(D∗D¯∗)−π+ indicates that a charged enhancement structure around D∗D¯∗ appears in the D∗D¯∗ invariant mass spectrum for this process, which might correspond to the newly observed Zc(4025) structure