Brane effects on extra-dimensional scenarios: a tale of two gravitons

We analyze the propagation of a scalar field in multidimensional theories which include kinetic corrections in the brane, as a prototype for gravitational interactions in a four-dimensional brane located in a (nearly) flat extra-dimensional bulk. We regularize the theory by introducing an infrared cutoff given by the size of the extra dimensions, R, and a physical ultraviolet cutoff of the order of the fundamental Planck scale in the higher-dimensional theory, M. We show that, having implemented cutoffs, the radius of the extra dimensions cannot be arbitrarily large for M≳1 TeV. Moreover, for finite radii, the gravitational effects localized on the brane can substantially alter the phenomenology of collider and/or table-top gravitational experiments. This phenomenology is dictated by the presence of a massless graviton, with standard couplings to the matter fields, and a massive graviton which couples to matter in a much stronger way. While graviton KK modes lighter than the massive graviton couple to matter in a standard way, the couplings to matter of the heavier KK modes are strongly suppressed.     

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.     

String-induced space compactification

Motivated by the possibility of a finite theory of gravity provided by superstrings in ten space-time dimensions, we analyze the problem of space compactification in the context of string dynamics. Such an analysis is hampered by conceptual and technical problems, stemming from the existence of the quantum string's own graviton mode on the one hand, and from Witten's observation of anomalies in a not specially chosen curves space-time on the other hand. Still, in the context of a classical local field presentation of string theory à la Nambu and Hosotani, supplemented by gravitational and Kalb-Ramond interactions, we are able to find solutions with space compactification. It is the antisymmetric tensor zero modes that dictate this compactification towards three space-time dimensions for ordinary strings or towards four or five space-time dimensions for superstrings.     

On the phenomenological three-graviton vertex

In General Relativity, the graviton interacts in three-graviton vertex with a tensor that is not the energy-momentum tensor of the gravitational field. We consider the possibility that the graviton interacts with the definite gravitational energy-momentum tensor that we previously found in the G ² approximation. This tensor in a gauge, where nonphysical degrees of freedom do not contribute, is remarkable, because it gives positive gravitational energy density for the Newtonian center in the same manner as the electromagnetic energy-momentum tensor does for the Coulomb center. We show that the assumed three-graviton vertex does not lead to contradiction with the precession of Mercury’s perihelion. In the S-matrix approach used here, the external gravitational field has only a subsidiary role, similar to the external field in quantum electrodynamics. This approach with the assumed vertex leads to the gravitational field that cannot be obtained from a consistent gravity equation.     

Gravitational contribution to the Casimir energy in Kaluza-Klein theories

The Casimir energy of the gravitational field in Kaluza-Klein theories is investigated. The mathematical techniques needed to compute the contribution of a single graviton loop to the quantum effective potential on a background manifold of (Minkowski space) ? (N-sphere) are developed. In these computations the cosmological constant plays a dynamical role, acting like a mass for the graviton. The numerical work for the case N = 1 is done explicitly, and a solution to the one-loop corrected equations of motion is found, although it is not stable. The possibility of an imaginary part to the effective potential for N > 1 is noted, and its existence is attributed to tachyonic terms in the mode sum.     

The problem of stability of the homogeneous and isotropic universe in the relativistic theory of gravitation

The problem of stability of the homogeneous and isotropic Universe with respect to small perturbations in the gravitational field and matter characteristics is studied in the framework of the relativistic theory of gravitation. The equations for small perturbations of the metric tensor g _μν, energy density ρ, and pressure p are obtained in the linear approximation. The solutions to these equations are found when perturbations depend only on time. The physical character of the obtained solutions is analyzed. A comparison with the results of General Relativity yields the conclusion that all differences are due to the graviton mass.     

Non critical super strings on world sheets of constant curvature

We consider correlation functions in Neveu-Schwarz string theory coupled to two dimensional gravity. The actionfor the 2D gravity consists of the string induced Liouville action and the Jackiw-Teitelboim action describing pure 2D gravity. Then gravitational dressed dimensions of vertex operators are equal to their bare conformal dimensions. There are two possible interpretations of the model. Considering the 2D dilaton and the Liouville field as additional target space coordinates one gets ad+2-dimensional critical string. In thed-dimensional non critical string picture gravitational fields retain their original meaning and ford=4 one can get a mass spectrum via consistency requirements. In both cases a GSO projection is possible.     

Configurational Entropy and Newton's Law in Double Sine‐Gordon Braneworlds

The Shannon‐like entropic measure of spatially localized functions for a 5D braneworld generated by a double sine‐Gordon (DSG) potential is evaluated. The differential configurational entropy (DCE) has been shown in several recent works to be a configurational informational measure (CIM) that selects critical points and brings out phase transitions in confined energy models with arbitrary parameters. The DSG scenario is selected because it presents an energy‐degenerate spatially localized profile where the solutions to the scalar field demonstrate critical behavior that is only a result of geometrical effects. As is shown, the DCE evaluation provides a method for predicting the existence of a transition between the phases of the domain wall solutions. Moreover, the entropic measure reveals information about the model that is capable of describing the phase sector where resonance modes on the massive spectra of the graviton is obtained. The graviton resonance lifetimes are related to the existence of scales on which 4D gravity is recovered. Thus, the critical points defined by the CIMs with the existence of resonances and their lifetimes are correlated. To extend the research regarding this system, the corrections to Newton's law coming from the graviton modes are calculated.     

Unimodular bimode gravity and the coherent scalar-graviton field as galaxy dark matter

An explicit violation of the general gauge invariance/relativity is adopted as the origin of dark matter and dark energy in the context of gravitation. The violation of the local scale invariance alone, with the residual unimodular one, is considered. Besides the four-volume preserving deformation mode—the transverse-tensor graviton—the metric comprises a compression mode—the scalar graviton, or the systolon. A unimodular invariant and general covariant metric theory of the bimode/scalar-tensor gravity is consistently worked out. To reduce the primordial ambiguity of the theory a dynamical global symmetry is imposed, with its subsequent spontaneous breaking revealed. The static spherically symmetric case in empty space, except possibly for the origin, is studied. A three-parameter solution describing a new static space structure—the dark lacuna—is constructed. It enjoys the property of gravitational confinement, with the logarithmic potential of gravitational attraction at the periphery, and results in asymptotically flat rotation curves. Comprising a super-massive dark fracture (a scalar-modified black hole) at the origin surrounded by a cored dark halo, the dark lacunas are proposed as a prototype model of galaxies, implying an ultimate account for the distributed non-gravitational matter and putative asphericity or rotation.     

Gravitation interactions at high energies and Reggeon scheme

A parton-Reggeon model that, for basic partons, employs gravitons of virtuality on the order of the Planck scale is proposed to describe inelastic interactions at trans-Planckian energies. A graviton analog of the Pomeron with an intercept of α(0)=3 is introduced on the basis of the structure of the gravitational field of a fast particle. Its unitarization leads to inelastic cross sections growing in proportion to s and corresponds to the pattern of a collision between black disks of radius about E _i ^1/2 . The inclusive spectra of hard gravitions whose behavior is determined by the size of the region of overlap of colliding black disks at various impact parameters and various energies is found. The graviton system formed in this way proves to be unstable against the gravitational attraction of particles having close momenta. This leads to the emergence of a multiperipheral chain of black holes at the stage of divergence—the structure of such a chain depends greatly on the impact parameters of a collision.     

Gravitational Waves and the Conformal Transformation

We study the problem of the behaviour of cosmological gravitational waves under conformal transformations. In spite of the apparent triviality of this question, the informations we can obtain from gravitational waves in the so-called Einstein's and Jordan's frame are not the same, mainly with respect to the choice of the initial conditions and of graviton production. The only exception seems to occur in string cosmology due to the duality properties.     

Double field formulation of Yang-Mills theory

Based on our previous work on the differential geometry for the closed string double field theory, we construct a Yang-Mills action which is covariant under O(D,D) T-duality rotation and invariant under three-types of gauge transformations: non-Abelian Yang-Mills, diffeomorphism and one-form gauge symmetries. In double field formulation, in a manifestly covariant manner our action couples a single O(D,D) vector potential to the closed string double field theory. In terms of undoubled component fields, it couples a usual Yang-Mills gauge field to an additional one-form field and also to the closed string background fields which consist of a dilaton, graviton and a two-form gauge field. Our resulting action resembles a twisted Yang-Mills action.     

General relativity with an auxiliary dimension

I consider an extension of General Relativity by an auxiliary nondynamical dimension that enables our space–time to acquire an extrinsic curvature. Obtained gravitational equations, without or with a cosmological constant, have a selfaccelerated solution that is independent of the value of the cosmological constant, and can describe the cosmic speedup of the Universe as a geometric effect. Background evolution of the selfaccelerated solution is identical to that of ordinary de Sitter space. I show that linear perturbations on this solution describe either a massless graviton, or a massive graviton and a scalar, which are free of ghosts and tachyons for certain choices of boundary conditions. The obtained linearized expressions suggest that nonlinear interactions should, for certain boundary conditions, be strongly coupled, although this issue is not studied here. The full nonlinear Hamiltonian of the theory is shown to be positive for the selfaccelerated solution, while in general, it reduces to surface terms in our and auxiliary dimensions.     

Holographic dual of de Sitter universe with AdS bubbles

We study the proposal that a de Sitter (dS) universe with an Anti-de Sitter (AdS) bubble can be replaced by a dS universe with a boundary CFT. To explore this duality, we consider incident gravitons coming from the dS universe through the bubble wall into the AdS bubble in the original picture. In the dual picture, this process has to be identified with the absorption of gravitons by CFT matter. We have obtained a general formula for the absorption probability in general d+1 spacetime dimensions. The result shows the different behavior depending on whether spacetime dimensions are even or odd. We find that the absorption process of gravitons from the dS universe by CFT matter is controlled by localized gravitons (massive bound state modes in the Kaluza-Klein decomposition) in the dS universe. The absorption probability is determined by the effective degrees of freedom of the CFT matter and the effective gravitational coupling constant which encodes information of localized gravitons. We speculate that the dual of (d+1)-dimensional dS universe with an AdS bubble is also dual to a d-dimensional dS universe with CFT matter.     

<Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity constraints from gravitational waves

The recent LIGO observation sparked interest in the field of gravitational wave signals. Besides the gravitational wave observation the LIGO collaboration used the inspiraling black hole pair to constrain the graviton mass. Unlike general relativity, f(R) theories have a characteristic non-zero mass graviton. We apply this constraint on the graviton mass to viable f(R) models in order to find the effects on model parameters. We find it possible to constrain the parameter space with these gravity wave based observations. We consider the popular Hu–Sawicki model as a case study and find an appropriate parameter bracket. The result generalizes to other f(R) theories and can be used to constrain the parameter space.     

On a Lagrangian formulation of gravitoelectromagnetism

We examine a Lagrangian formulation of gravity based on an approach analogous to electromagnetism, called Gravitoelectromagnetism (GEM). The gravitational analogue of the electromagnetic field tensor is a three-index tensor, \({\mathcal {F}_{\mu\nu\lambda}}\), defined in terms of a two-index gravitoelectromagnetic potential, \({\mathcal {A}_{\mu\nu}}\). The energy-momentum tensor is derived and is symmetric. We construct a Lagrangian which allows us to describe interactions between fermions, photons and gravitons. We calculate transition amplitudes of various processes involving gravitons: gravitational Møller scattering, gravitational Compton scattering, and the graviton photoproduction.     

Non-linear sigma model in 1 + 1 dimensions,supergravity and the spinning string

The non-linear σ supersymmetric model in 1 + 1 dimensions is coupled to supergravity. When we quantize the theory, the matter fields acquire mass dynamically, which leads to the breaking of the Weyl invariance. This fact implies that the two-point functions of the gravitino and the graviton, obtained from the effective action, become non-trivial. Particularly, the two-point function of the gravitino presents a pole in the infrared region. We conjecture that this pole is related to the confinement of all supersymmetric degrees of freedom of the theory. If we restrain the integration domain of x₁ to a finite length L (breaking all invariances of the theory), there appears a mass term in the two-point function of the gravitino, which decreases exponentially with L. In this context we relate this model with that of the supersymmetric string and define a stability criterion for the latter.     

Heterotic string dark matter from the graviton multiplet

In the string theory framework for physics beyond the standard model the hidden sector of E₈×E₈ heterotic string theory and the graviton multiplet provide compelling sources for the dark matter in the universe.

In the present investigation I consider the graviton multiplet as one particular dark matter source in heterotic string theory. In particular, it is pointed out that an appreciable fraction of dark matter from the graviton multiplet requires a mass generating phase transition around T_c10⁸ GeV, where the symmetry partners of the graviton would evolve from an ultrahard fluid to pressureless dark matter. This indicates m10 MeV for the massive components of the graviton multiplet, and it is reassuring that the corresponding dilaton lifetime τ10¹⁷ s is compatible with a dark matter interpretation.