Radion‐induced gravitational wave oscillations and their phenomenology

We discuss the theory and phenomenology of the interplay between the massless graviton and its massive Kaluza‐Klein modes in the Randall‐Sundrum two‐brane model. The equations of motion of the transverse traceless degrees of freedom are derived by means of a Green function approach as well as from an effective nonlocal action. The second procedure clarifies the extraction of the particle content from the nonlocal action and the issue of its diagonalization. The situation discussed is generic for the treatment of two‐brane models if the on‐brane fields are used as the dynamical degrees of freedom. The mixing of the effective graviton modes of the localized action can be interpreted as radion‐induced gravitational‐wave oscillations, a classical analogy to meson and neutrino oscillations. We show that these oscillations arising in M‐theory‐motivated braneworld setups could lead to effects detectable by gravitational‐wave interferometers. The implications of this effect for models with ultra‐light gravitons are discussed.     

Mass hierarchy, mass gap and corrections to Newton’s law on thick branes with Poincaré symmetry

We consider a scalar thick brane configuration arising in a 5D theory of gravity coupled to a self-interacting scalar field in a Riemannian manifold. We start from known classical solutions of the corresponding field equations and elaborate on the physics of the transverse traceless modes of linear fluctuations of the classical background, which obey a Schrödinger-like equation. We further consider two special cases in which this equation can be solved analytically for any massive mode with $m^2\ge 0$ , in contrast with numerical approaches, allowing us to study in closed form the massive spectrum of Kaluza–Klein (KK) excitations and to analytically compute the corrections to Newton’s law in the thin brane limit. In the first case we consider a novel solution with a mass gap in the spectrum of KK fluctuations with two bound states—the massless 4D graviton free of tachyonic instabilities and a massive KK excitation—as well as a tower of continuous massive KK modes which obey a Legendre equation. The mass gap is defined by the inverse of the brane thickness, allowing us to get rid of the potentially dangerous multiplicity of arbitrarily light KK modes. It is shown that due to this lucky circumstance, the solution of the mass hierarchy problem is much simpler and transparent than in the thin Randall–Sundrum (RS) two-brane configuration. In the second case we present a smooth version of the RS model with a single massless bound state, which accounts for the 4D graviton, and a sector of continuous fluctuation modes with no mass gap, which obey a confluent Heun equation in the Ince limit. (The latter seems to have physical applications for the first time within braneworld models). For this solution the mass hierarchy problem is solved with positive branes as in the Lykken–Randall (LR) model and the model is completely free of naked singularities. We also show that the scalar–tensor system is stable under scalar perturbations with no scalar modes localized on the braneworld configuration.     

Prospects for identification the direct and indirect effects of extra spatial dimensions at the Large Hadron Collider

The existence of massive graviton states, that may be produced as real and virtual particles in high-energy proton collisions, is predicted by the modern developments of Kaluza–Klein models with extra spatial dimensions. The direct and indirect signatures of large and warped extra spatial dimensions may be revealed by analyzing the specific characteristics of dilepton and diphoton final states formed in proton–proton collisions at the Large Hadron Collider (LHC). Virtual effects in the Kaluza–Klein models with large extra spatial dimensions can be discovered by the specic behavior of the dilpton and diphoton invariant-mass distributions, and their identication (in case of discovery) can be performed by the analysis of their angular distributions with integrated center-edge asymmetry. Assuming the nominal values of the LHC collision energy (14 TeV) and luminosity (100 fb^–1), for the models with large extra spatial dimensions we find that the sensitivity to the cutoff parameter M _S will extend up to 8.5 and 7.6 TeV for their discovery and identification, respectively. For the Randall–Sundrum model with a warped extra dimension, the LHC experiments will be sensitive to the graviton resonance with mass up to 4.4 and 3.1 TeV for its discovery and identification, respectively.     

On superplanckian scattering on the brane

The multidimensional space-time with (D-4) compact extra space dimensions and SM fields confined on a four-dimensional brane is considered. The elastic scattering amplitude of two particles interacting by gravitational forces is calculated at superplanckian energies. Particular attention is paid to a proper account of zero (massless) graviton mode. The renormalized Born pole is reproduced in the eikonal amplitude which makes a leading contribution at small momentum transfers. This singular part of the amplitude coincides with well-known D-dimensional amplitude taken at . The expression for the contribution from massive graviton modes to the eikonal is derived, and its asymptotics in the impact parameter is calculated. Our formula gives the correct four-dimensional expression at , where R_c is the radius of the higher dimensions. The results are also compared with those obtained previously for the scattering of the bulk fields in flat extra dimensions.Received: 9 September 2003, Revised: 2 February 2004, Published online: 2 April 2004     

Our world as an intersection of walls and a string

A solution of Einstein equations is obtained for our four-dimensional world as an intersection of a wall and a string-like defect in seven-dimensional spacetime with a negative cosmological constant. A matter energy–momentum tensor localized on the wall and on the string is needed. A single massless graviton is found and is localized around the intersection. The leading correction to the gravitational Newton potential from massive spin 2 graviton is found to be almost identical to that of a wall in five dimensions, contrary to the case of a string in six dimensions. The generalization to the intersection of a string and n orthogonally intersecting walls is also obtained and a similar result is found for the gravitational potential.     

Detecting extra dimensions with gravity-wave spectroscopy: the black-string brane world

Using the black string between two branes as a model of a brane-world black hole, we compute the gravity-wave perturbations and identify the features arising from the additional polarizations of the graviton. The standard four-dimensional gravitational wave signal acquires late-time oscillations due to massive modes of the graviton. The Fourier transform of these oscillations shows a series of spikes associated with the masses of the Kaluza-Klein modes, providing in principle a spectroscopic signature of extra dimensions.     

Massive graviton as a testable cold-dark-matter candidate

We construct a consistent model of gravity where the tensor graviton mode is massive, while linearized equations for scalar and vector metric perturbations are not modified. The Friedmann equation acquires an extra dark-energy component leading to accelerated expansion. The mass of the graviton can be as large as approximately (10(15) cm)(-1), being constrained by the pulsar timing measurements. We argue that nonrelativistic gravitational waves can comprise the cold dark matter and may be detected by the future gravitational wave searches.     

Kaluza–Klein modes of bulk fields in a generalized Randall–Sundrum scenario

We consider a generalised two brane Randall–Sundrum model with non-zero cosmological constant on the visible TeV brane. Massive Kaluza–Klein modes for various bulk fields namely graviton, gauge field and antisymmetric second rank Kalb–Ramond field in a such generalized Randall–Sundrum scenario are determined. The masses for the Kaluza–Klein excitations of different bulk fields are found to depend on the brane cosmological constant indicating interesting consequences in warped brane particle phenomenology.     

Tensor gauge field localization on a string-like defect

This work is devoted to the study of tensor gauge fields on a string-like defect in six dimensions. This model is very successful in localizing fields of various spins only by gravitational interaction. Due to problems of field localization in membrane models we are motivated to investigate if a string-like defect localizes the Kalb–Ramond field. In contrast to what happens in Randall–Sundrum and thick brane scenarios we find a localized zero mode without the addition of other fields in the bulk. Considering the local string defect we obtain analytical solutions for the massive modes. Also, we take the equations of motion in a supersymmetric quantum mechanics scenario in order to analyze the massive modes. The influence of the mass as well as the angular quantum number in the solutions is described. An additional analysis on the massive modes is performed by the Kaluza–Klein decomposition, which provides new details about the KK masses.     

3D black holes on a 2-brane in 4D Minkowski space

We investigate three-dimensional black hole solutions in the realm of pure and new massive gravity in 2+1 dimensions induced on a 2-brane embedded in a flat four-dimensional spacetime. There is no cosmological constant neither on the brane nor on the four-dimensional bulk. Only gravitational fields are turned on and we indeed find vacuum solutions as black holes in 2+1 dimensions even in the absence of any cosmological solution. There is a crossover scale that controls how far the three- or four-dimensional gravity manifests on the 2-brane. Our solutions also indicate that local BTZ and SdS₃ solutions can flow to local four-dimensional Schwarzschild-like black holes, as one probes from small to large distances, which is clearly a higher dimensional manifestation on the 2-brane. This is similar to the DGP scenario where the effects of extra dimensions for large probed distances along the brane manifest.     

Gravity localization in sine-Gordon braneworlds

In this work we study two types of five-dimensional braneworld models given by sine-Gordon potentials. In both scenarios, the thick brane is generated by a real scalar field coupled to gravity. We focus our investigation on the localization of graviton field and the behaviour of the massive spectrum. In particular, we analyse the localization of massive modes by means of a relative probability method in a Quantum Mechanics context. Initially, considering a scalar field sine-Gordon potential, we find a localized state to the graviton at zero mode. However, when we consider a double sine-Gordon potential, the brane structure is changed allowing the existence of massive resonant states. The new results show how the existence of an internal structure can aid in the emergence of massive resonant modes on the brane.     

Effective field theory for massive gravitons and gravity in theory space

We introduce a technique for restoring general coordinate invariance into theories where it is explicitly broken. This is the analog for gravity of the Callan-Coleman-Wess-Zumino formalism for gauge theories. We use this to elucidate the properties of interacting massless and massive gravitons. For a single graviton with a Planck scale M_Pl and a mass m_g, we find that there is a sensible effective field theory which is valid up to a high-energy cutoff Λ parametrically above m_g. Our methods allow for a transparent understanding of the many peculiarities associated with massive gravitons, among them the need for the Fierz-Pauli form of the Lagrangian, the presence or absence of the van Dam-Veltman-Zakharov discontinuity in general backgrounds, and the onset of non-linear effects and the breakdown of the effective theory at large distances from heavy sources. The natural sizes of all non-linear corrections beyond the Fierz-Pauli term are easily determined. The cutoff scales as Λ∼(m_g⁴M_Pl)^1/5 for the Fierz-Pauli theory, but can be raised to Λ∼(m_g²M_Pl)^1/3 in certain non-linear extensions. Having established that these models make sense as effective theories, there are a number of new avenues for exploration, including model building with gravity in theory space and constructing gravitational dimensions.     

Dynamical casimir effect in braneworlds

In braneworld cosmology the expanding Universe is realized as a brane moving through a warped higher-dimensional spacetime. Like a moving mirror causes the creation of photons out of vacuum fluctuations, a moving brane leads to graviton production. We show that, very generically, Kaluza-Klein (KK) particles scale like stiff matter with the expansion of the Universe and can therefore not represent the dark matter in a warped braneworld. We present results for the production of massless and KK gravitons for bouncing branes in five-dimensional anti-de Sitter space. We find that for a realistic bounce the back reaction from the generated gravitons will be most likely relevant. This Letter summarizes the main results and conclusions from numerical simulations which are presented in detail in a long paper [M. Ruser and R. Durrer, arXiv:0704.0790].     

Brane gravitational interactions from 6D supergravity

We investigate the massive graviton contributions to 4D gravity in a 6D brane world scenario, whose bulk field content can include that of 6D chiral gauged supergravity. We consider a general class of solutions having 3-branes, 4D Poincaré symmetry and axisymmetry in the internal space. We show that these contributions, which we compute analytically, can be independent of the brane vacuum energy as a consequence of geometrical and topological properties of the above-mentioned codimension two brane world. These results support the idea that in such models the gravitational interactions may be decoupled from the brane vacuum energy.     

4D gravity on a BPS brane in 5D AdS-Minkowski space

We calculate small correction terms to gravitational potential near an asymmetric BPS brane embedded in a 5D AdS-Minkowski space in the context of supergravity. The normalizable wave functions of gravity fluctuations around the brane describe only massive modes. We compute such wave functions analytically in the thin wall limit. We estimate the correction to gravitational potential for small and long distances, and show that there is an intermediate range of distances in which we can identify 4D gravity on the brane below a crossover scale. The 4D gravity is metastable and for distances much larger than the crossover scale the 5D gravity is recovered.     

Nonsaturation of the J/psi suppression at large transverse energy in the comovers approach

We explore the phenomenology of the localized gravity model of Randall and Sundrum where a 5-dimensional nonfactorizable geometry generates the gauge hierarchy by an exponential function called a warp factor. The Kaluza-Klein (KK) tower of gravitons in this scenario has different properties from those in factorizable models. We derive the KK graviton interactions with the standard model fields and obtain constraints from their direct production at hadron colliders as well as from virtual KK exchanges. We study the KK spectrum in e(+)e(-) annihilation and show how to determine the model parameters if the first KK state is observed.     

From massive gravity to modified general relativity II

We continue our investigation of massive gravity in the massless limit of vanishing graviton mass. From gauge invariance we derive the most general coupling between scalar matter and gravity. We get further couplings beside the standard coupling to the energy–momentum tensor. On the classical level this leads to a further modification of general relativity.     

Brane World Corrections to Newton’s Law

We discuss possible variations of the effective gravitational constant with length scale, predicted by most of alternative theories of gravity and unified models of physical interactions. After giving a brief general exposition, we review in more detail the predicted corrections to Newton’s law of gravity in diverse brane world models. We consider various configurations in 5 dimensions (flat, de Sitter and AdS branes in Einstein and Einstein–Gauss–Bonnet theories, with and without induced gravity and possible incomplete graviton localization), 5D multi-brane systems and some models in higher dimensions. A common feature of all models considered is the existence of corrections to Newton’s law at small radii comparable with the bulk characteristic length: at such radii, gravity on the brane becomes effectively multidimensional. Many models contain superlight perturbation modes, which modify gravity at large scale and may be important for astrophysics and cosmology.     

Resonances of Spin-1/2 Fermions in Eddington-Inspired Born-Infeld Gravity

We investigate the fermionic resonances for both chiralities in five-dimensional Eddington-inspired BornInfeld(EiBI)theory.In order to localize fermion on the brane,it needs to be considered the Yukawa coupling between the fermion and the background scalar field.In our models,since the background scalar field has kink,double kink,or anti-kink solution,the system has rich resonant Kaluza-Klein(KK)modes structure.The massive KK fermionic modes feel a volcano potential,which result in a fermionic zero mode and a set of continuous massive KK modes.The inner structure of the branes and a free parameter in background scalar field influence the resonant behaviors of the massive KK fermions.