Modified gravity on the brane and dark energy

We analyze the dynamics of an AdS₅ braneworld with matter fields when gravity is allowed to deviate from the Einstein form on the brane. We consider exact five-dimensional warped solutions which are associated with conformal bulk fields of weight –4 and describe on the brane the following three dynamics: those of inhomogeneous dust, of generalized dark radiation, and of homogeneous polytropic dark energy. We show that, with modified gravity on the brane, the existence of such dynamical geometries requires the presence of non-conformal matter fields confined to the brane.     

Braneworld model of dark matter: structure formation

Following a previous work (García-Aspeitia in Gen Rel Grav 43:315–329, 2011), we further study the behavior of a real scalar field in a hidden brane in a configuration of two branes embedded in a five dimensional bulk. We find an expression for the equation of state for this scalar field in the visible brane in terms of the fields of the hidden one. Additionally, we investigated the perturbations produced by this scalar field in the visible brane with the aim to study their dynamical properties. Our results show that if the kinetic energy of the scalar field dominates during the early universe the perturbed scalar field could mimic the observed dynamics for the dark matter in the standard paradigm. Thus, the scalar field dark matter hypothesis in the context of braneworld theory could be an interesting alternative to the nature of dark matter in the Universe.     

de Sitter branes with a bulk scalar

We propose new brane world models arising from a scalar field in the bulk. In these examples, the induced on-brane line element is de Sitter (or anti de Sitter) and the bulk (five dimensional) Einstein equations can be exactly solved to obtain warped spacetimes. The solutions thus derived are single and two-brane models—one with thin branes while the other one of the thick variety. The field profiles and the potentials are obtained and analysed for each case. We note that for the thick brane scenario the field profile resembles a kink, whereas for one or more thin branes, it is finite and bounded in the domain of the extra dimension. We have also addressed the localisation of gravity and other matter fields on the brane for these braneworld models.     

K-essential covariant holography

Braneworld models may yield interesting effects ranging from high-energy physics to cosmology, or even some low-energy physics. Their mode structure modifies standard results in these physical realms that can be tested and used, for example, to set bounds on the models parameters. Now, to define braneworld deviations from standard 4D physics, a notion of matter and gravity localization on the brane is crucial. In this work we investigate the localization of universal massive scalar fields in a de Sitter thick tachyonic braneworld generated by gravity coupled to a tachyonic bulk scalar field. This braneworld possesses a 4D de Sitter induced metric and is asymptotically flat despite the presence of a negative bulk cosmological constant, a novel and interesting peculiarity that contrasts with previously known models. It turns out that universal scalar fields can be localized in this expanding braneworld if their bulk mass obeys an upper bound, otherwise the scalar fields delocalize: The dynamics of the scalar field is governed by a Schrödinger equation with an analog quantum mechanical potential of modified Pöschl–Teller type. This potential depends on the bulk curvature of the braneworld system as well as on the value of the bulk scalar field mass. For masses satisfying a certain upper bound, the potential displays a negative minimum and possesses a single massless bound state separated from the Kaluza–Klein (KK) massive modes by a mass gap defined by the Hubble (expansion scale) parameter of the 3-brane. As the bulk scalar field mass increases, the minimum of the quantum mechanical potential approaches a null value and, when the bulk mass reaches certain upper bound, it becomes positive (eventually transforming into a potential barrier), leading to delocalization of the bulk scalar field from the brane. We present analytical expressions for the general solution of the Schrödinger equation. Thus, the KK massive modes are given in terms of general Heun functions as well as the expression for the massless zero mode, giving rise to a new application of these special functions.     

Cosmological Kaluza–Klein branes in black brane spacetimes

We discuss the cosmological evolution of a brane in the D(>6)$D(>6)$-dimensional black brane spacetime in the context of the Kaluza–Klein (KK) braneworld scheme, i.e., to consider KK compactification on the brane. The bulk spacetime is composed of two copies of a patch of D  -dimensional black three-brane solution. The near-horizon geometry is given by AdS₅×S(D−5)${\mathit{AdS}}_5\times S^{(D-5)}$ while in the asymptotic infinity the spacetime approaches D-dimensional Minkowski. We consider the brane motion from the near-horizon region toward the spatial infinity, which induces cosmology on the brane. As is expected, in the early times, namely when the brane is located in the near-horizon region, the effective cosmology on the brane coincides with that in the second Randall–Sundrum (RS II) model. Then, the brane cosmology starts to deviate from the RS type one since the dynamics of KK compactified dimensions becomes significant. We find that the brane Universe cannot reach the asymptotic infinity, irrespectively of the components of matter on the brane.     

Universal torsion-induced interaction from large extra dimensions

We consider the Kaluza-Klein (KK) scenario in which only gravity exists in the bulk. Without the assumption of symmetric connection, the presence of brane fermions induces torsion. The result is a universal axial contact interaction that dominates those induced by KK gravitons. This enhancement arises from a large spin density on the brane. Using a global fit to Z-pole observables, we find the 3sigma bound on the scale of quantum gravity to be 28 TeV for n = 2. If Dirac or light sterile neutrinos are present, the data from SN1987A increase the bound to sqrt[n] M(S)>/=210 TeV.     

Shortcuts in Cosmological Branes

We aim at gathering information from gravitational interaction in the Universe, at energies where quantum gravity is required. In such a setup a dynamical membrane world in a space-time with scalar bulk matter described by domain walls, as well as a dynamical membrane world in empty Anti de Sitter space-time, is analyzed. We later investigate the possibility of having shortcuts for gravitons leaving the membrane and returning subsequently. In comparison with photons following a geodesic inside the brane, we verify that shortcuts exist. For late time universes they are small, but for some primordial universes they can be quite effective. In the case of matter branes, we argue that at times just before nucleosynthesis the effect is sufficiently large to provide corrections to the inflationary scenario, especially as concerning the horizon problem and the Cosmological Background Radiation.     

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.     

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.     

A Cosmological Model of Holographic Brane Gravity

A cosmological scenario with two branes (A and B) moving in a 5-dimensional bulk is considered. As in the case of ecpyrotic and born-again braneworld models it is possible that the branes collide. The energy-momentum tensor is taken to describe a perfect barotropic fluid on the A-brane and a phenomenological time-dependent cosmological constant on the B-brane. The A-brane is identified with our Universe and its cosmological evolution in the approximation of a homogeneous and isotropic brane is analysed. The dynamics of the radion (a scalar field on the brane) contains information about the proper distance between the branes. It is demonstrated that the deSitter type solutions are obtained for late time evolution of the braneworld and accelerative behaviour is anticipated at the present time.     

The cosmological constant and dark energy in braneworlds

We review recent attempts to address the cosmological constant problem and the late-time acceleration of the Universe based on braneworld models. In braneworld models, the way in which the vacuum energy gravitates in the 4D spacetime is radically different from conventional 4D physics. It is possible that the vacuum energy on a brane does not curve the 4D spacetime and only affects the geometry of the extra-dimensions, offering a solution to the cosmological constant problem. We review the idea of supersymmetric large extra dimensions that could achieve this and also provide a natural candidate for a quintessence field. We also review the attempts to explain the late-time accelerated expansion of the universe from the large-distance modification of gravity based on the braneworld. We use the Dvali–Gabadadze–Porrati model to demonstrate how one can distinguish this model from dark energy models in 4D general relativity. Theoretical difficulties in this approach are also addressed.     

Does Unruh radiation accelerate the universe? A novel approach to the cosmic acceleration

We present a novel mechanism for the present acceleration of the universe. We find that the temperature of the Unruh radiation perceived by the brane is not equal to the inherent temperature (Hawking temperature at the apparent horizon) of the brane universe in the frame of Dvali–Gabadadze–Porrati (DGP) braneworld model. The Unruh radiation perceived by a dust dominated brane is always warmer than the brane measured by the geometric temperature, which naturally induces an energy flow between bulk and brane based on the most sound thermodynamics principles. Through a thorough investigation to the microscopic mechanism of interaction between bulk Unruh radiation and brane matter, we put forward that an energy influx from bulk Unruh radiation to the dust matter on the brane accelerates the universe.     

Non-minimal warm inflation and perturbations on the warped DGP brane with modified induced gravity

We construct a warm inflation model with inflaton field non-minimally coupled to induced gravity on a warped DGP brane. We incorporate possible modification of the induced gravity on the brane in the spirit of f(R)-gravity. We study cosmological perturbations in this setup. In the case of two field inflation such as warm inflation, usually entropy perturbations are generated. While it is expected that in the case of one field inflation these perturbations to be removed, we show that even in the absence of the radiation field, entropy perturbations are generated in our setup due to non-minimal coupling and modification of the induced gravity. We study the effect of dissipation on the inflation parameters of this extended braneworld scenario.     

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.     

Localization of Matter Fields in the 6D Standing Wave Braneworld

We introduce new 6D standing wave braneworld model generated by gravity coupled to a phantom-like scalar field and investigate the problem of pure gravitational localization of matter fields. We show that in the case of increasing warp factor spin 0, 1, 1/2 and 2 fields are localized on the brane.     

Inflation and late-time acceleration in braneworld cosmological models with varying brane tension

Braneworld models with variable brane tension λ introduce a new degree of freedom that allows for evolving gravitational and cosmological constants, the latter being a natural candidate for dark energy. We consider a thermodynamic interpretation of the varying brane tension models, by showing that the field equations with variable λ can be interpreted as describing matter creation in a cosmological framework. The particle creation rate is determined by the variation rate of the brane tension, as well as by the brane–bulk energy-matter transfer rate. We investigate the effect of a variable brane tension on the cosmological evolution of the Universe, in the framework of a particular model in which the brane tension is an exponentially dependent function of the scale factor. The resulting cosmology shows the presence of an initial inflationary expansion, followed by a decelerating phase, and by a smooth transition towards a late accelerated de Sitter type expansion. The varying brane tension is also responsible for the generation of the matter in the Universe (reheating period). The physical constraints on the model parameters, resulting from the observational cosmological data, are also investigated.     

Modified gravitational equations on braneworld with Lorentz invariant violation

The modified gravitational equations to describe a four-dimensional braneworld in the case with the Lorentz invariant violation in a bulk spacetime is presented. It contains a trace part of the brane energy-momentum tensor and the coefficients of all terms describe the Lorentz violation effects from the bulk spacetime. As an application, we apply this formalism to study cosmology. In respect to standard effective Friedmann equations on the brane, Lorentz invariance violation in the bulk causes a modification of this equations that can lead to significant physical consequences. In particular, the effective Friedmann equation on the brane explicitly depends on the equation of state of the brane matter and the Lorentz violating parameters. We show that the components of five-dimensional Weyl curvature are related to the matter on brane even at low energies. We also find that the constraints on the theory parameters are depend on the equation of state of the energy components of the brane matter. Finally, the stability of the model depend on the specific choices of initial conditions and the parameters β _i .     

An Exact Class of Bulk Field Potentials onto the 5D-Warp of de Sitter Spacetime

In the five-dimensionally warped FRW Universe, we integrate the corresponding Einstein equations for a scalar source depending only on the extra-dimension. It yields a de Sitter brane and a specific warp factor for which we derive the effective bulk field potentials. These are generalizing some of the previously proposed forms in the literature.     

Gauge Model with Massive Gravitons

Gauge theory of gravity is formulated based on principle of local gauge invariance. Because the model hasstrict local gravitational gauge symmetry, and gauge theory of gravity is a perturbatively renormalizable quantum model.However, in the original model, all gauge gravitons are massless. We want to ask whether there exist massive gravitonsin Nature. In this paper, we will propose a gauge model with massive gravitons. The mass term of gravitational gaugefield is introduced into the theory without violating the strict local gravitational gauge symmetry. Massive gravitons canbe considered to be possible origin of dark energy and dark matter in the Universe.     

Search for Randall-Sundrum gravitons in dilepton and diphoton final states

We report the first direct search for the Kaluza-Klein (KK) modes of Randall-Sundrum gravitons using dielectron, dimuon, and diphoton events observed with the D0 detector operating at the Fermilab Tevatron pp(-) Collider at sqrt[s]=1.96 TeV. No evidence for resonant production of gravitons has been found in the data corresponding to an integrated luminosity of approximately equal to 260 pb(-1). Lower limits on the mass of the first KK mode at the 95% C.L. have been set between 250 and 785 GeV, depending on its coupling to standard model particles.