Warped Braneworld Research Articles

Braneworlds in warped Einsteinian cubic gravity

Einstenian cubic gravity (ECG) is a modified theory of gravity constructed with cubic contractions of the curvature tensor. This theory has the remarkable feature of having the same two propagating degrees of freedom of Einstein gravity (EG), at the perturbative level on maximally symmetric spacetimes. The additional unstable modes steaming from the higher order derivative dynamics are suppressed provided that we consider the ECG as an effective field theory wherein the cubic terms are seen as perturbative corrections of the Einstein-Hilbert term. Extensions of ECG have been proposed in cosmology and compact objects in order to probe if this property holds in more general configurations. In this work, we construct a modified ECG gravity in a five dimensional warped braneworld scenario. By assuming a specific combination of the cubic parameters, we obtained modified gravity equations of motion with terms up to second-order. For a thin 3-brane, the cubic-gravity corrections yield an effective positive bulk cosmological constant. Thus, in order to keep the 5D bulk warped compact, an upper bound of the cubic parameter with respect to the bulk curvature was imposed. For a thick brane, the cubic-gravity terms modify the scalar field potential and its corresponding vacuum. Nonetheless, the domain-wall structure with a localized source is preserved. At the perturbative level, the Kaluza-Klein (KK) tensor gravitational modes are stable and possess a localized massless mode provided the cubic corrections are small compared to the EG braneworld.

Nested warped geometry in a non-flat braneworld scenario

We generalize nested multiply warped braneworld models by incorporating non-zero brane curvature caused by an effective cosmological constant Omega induced on the 3-branes. Starting with the doubly warped model, we first analyze the case where the maximally warped brane is identified as the visible brane. For Omega <0, resolution of the gauge hierarchy problem imposes a small upper bound on |Omega |, and can possibly lead to positivity of all the 3-brane tensions. For Omega >0, the latter is not possible but the tuning of the cosmological constant to its tiny observed value is linked to the tuning of the extra dimensional moduli close to the inverse Planck length, justifying the original flat brane approximation. In both regimes, we study the dependence of the scale-clustering of the pair of TeV-branes on the brane cosmological constant and hence its potential role in generating a fermion mass hierarchy between these branes. Identifying the near-maximally warped brane as the visible brane instead opens up regions in the parameter space that allow positive 3-brane tensions for both anti de Sitter and de Sitter branes, subject to non-trivial constraints on the warping parameters. We conclude by generalizing the key results to arbitrary n-fold nested warped braneworlds.

Moduli stabilization with bulk scalar in nested doubly warped braneworld model

We examine the modulus stabilization mechanism of a warped geometry model with nested warping. Such a model with multiple moduli is known to offer a possible resolution of the fermion mass hierarchy problem in the Standard Model. A six dimensional doubly warped braneworld model under consideration admits two distinct moduli, with the associated warp factors dynamically generating different physical mass scales on four 3-branes. In order to address the hierarchy problem related to the Higgs mass, both moduli need to be stabilized around their desired values without any extreme fine tuning of parameters. We show that it is possible to stabilize them simultaneously due to the appearence of an effective 4D moduli potential, which is generated by a single massive bulk scalar field having non-zero VEVs frozen on the 3-branes. This gives rise to two scalar radions, one of which has mass slightly below {mathcal {O}}(TeV) and couplings to SM fields proportional to the inverse of its {mathcal {O}}(TeV) VEV, and the other has nearly {mathcal {O}}(M_{Pl}) mass and interactions with SM fields suppressed by the Planck scale. We also discuss how the entire mechanism can possibly be understood from a purely gravitational point of view, with higher curvature f(R) contributions in the bulk automatically providing a scalar degree of freedom that can serve as the stabilizing field in the Einstein frame.

Torsion braneworlds in a tensor-vector gravity

In this paper, we study the properties of gravity and bulk fields living in a torsion warped braneworld. The torsion is driven by a background vector whose norm provides a source for the bulk cosmological constant. For a vector as the derivative of a scalar field, we find new isotropic thick brane geometry. We analyze the features of bosonic and fermionic fields in this scenario. The background vector provides nonminimal coupling between the fields and the geometry leading to modifications in the Kaluza–Klein (KK) states. For a scalar field, the background vector breaks the [Formula: see text] symmetry, whereas for the vector gauge field, a geometric coupling to the torsion tensor traps the massless mode. The spinor connection is modified by the torsion and a geometric derivative Yukawa-like coupling is proposed. The effects of these new couplings are investigated.

Analytical solutions for bosonic fields in the cosmological multiply warped braneworld

In this paper, we find analytical solutions for the scalar and gauge fields in the cosmological multiply warped braneworld scenario. Having done that, we find the precise mass spectra for Bosonic fields. We compare those spectra to the ones previously found in the literature for the static case.

Thick string-like braneworlds in f(T) gravity

We propose a codimension two warped braneworld model within the teleparallel [Formula: see text] gravity. Asymptotically, the bulk geometry converges to an [Formula: see text] spacetime whose cosmological constant is produced by the torsion parameters. Furthermore, the torsion induces an AdS-dS transition on the exterior region. As the torsion parameters vary, the brane undergoes a phase transition from a thick string-like brane into ring-like structures. The bulk-brane Planck mass ration is modified by the torsion. The analysis of the stress–energy condition reveals a splitting brane process satisfying the weak and strong–energy conditions for some values of the parameters. In addition, we investigate the behavior of the gravitational perturbations in this scenario. It turns out that the gravitational spectrum has a linear behavior for small masses and is independent of the torsion parameters for large masses. In the bulk, the torsion keeps a gapless nonlocalizable and stable tower of massive modes. Inside the brane core, the torsion produces new barriers and potential wells leading to small amplitude massive modes and a massless mode localized around the ring structures.

Bouncing cosmology in a curved braneworld

We explore the possibility of a non-singular bounce in our universe from a warped braneworld scenario with dynamical branes and a non-zero brane cosmological constant. Such models naturally incorporate a scalar sector known as the radion originating from the modulus of the theory. The presence of brane cosmological constant renders the branes to be non-flat and gives rise to a potential and a non-canonical kinetic term for the radion field in the four dimensional effective action. The kinetic term exhibits a phantom-like behavior within the domain of evolution of the modulus which leads to a violation of the null-energy condition often observed in a bouncing universe. The interplay of the radion potential and kinetic term enables the evolution of the radion field from a normal to a phantom regime where the universe transits from a contracting era to an expanding epoch through a non-singular bounce. Analysis of the scalar and tensor perturbations over such background evolution reveal that the primordial observables e.g., the amplitude of scalar perturbations \U0001d49cs, tensor to scalar ratio r and the scalar spectral index ns are in agreement with the current constraints reported by the Planck satellite. The implications are discussed.

Braneworld effective field theories \u2014 holography, consistency and conformal effects

Braneworld theories are often described as low-energy effective field theories (EFTs) featuring an infinitely thin 3-brane and 4D fields exactly localized on it. We investigate whether an exactly localized braneworld can arise as a limit of a theory of 5D fields. Using a holographic formalism we argue that such limit does not exist in the presence of gravity, therefore implying a discontinuity in the space of EFTs. We then present specific models involving exactly localized fields in which inconsistencies appear, which are solved when fields are taken as quasilocalized. Part of our arguments rely on conjectures from the “swampland” program. Our investigation motivates braneworld EFTs built from 5D fields, i.e. quasilocalized braneworlds. Observable effects from quasilocalization are significant for warped braneworlds such as Randall-Sundrum II (RSII), and are reminiscent of a conformal hidden sector. Focusing on the gauge-gravity sector we show that manifestations of the quasilocalized warped braneworld include i) an anomalous running of SM gauge couplings ii) a conformal contribution to SM gauge boson scattering induced by 5D gravity. Constraining these effects puts an upper bound on the 5D EFT cutoff, implying that the warped braneworld hypothesis could — at least in principle — be tested completely.

Radion induced inflation on nonflat brane and modulus stabilization

Warped braneworld models has the potential to provide a plausible resolution to the gauge hierarchy problem but at the cost of introduction of an additional field, namely the inter-brane separation or, the radion field. Providing an appropriate stabilization scheme for the radion field has long been sought for. In this work, we discuss dynamical stabilization of the radion field in the context of early universe cosmology. We show that by allowing the branes to be \emph{non-flat} and \emph{dynamical} a radion potential is naturally generated which can trigger the inflationary phase of the early universe. Interestingly, the kinetic term of the radion during the inflationary epoch exhibits a phantom-like behavior and the dynamical evolution of the radion field to its stable value marks the exit from the phantom phase as well as the inflationary era simultaneously. We show that the amalgamation and synergy of the radion potential along with its kinetic term can not only trigger the inflationary scenario but also provide a successful exit from the same while maintaining concordance with current observation.

Modulus stabilization in a non-flat warped braneworld scenario

The stability of the modular field in a warped brane world scenario has been a subject of interest for a long time. Goldberger and Wise (GW) proposed a mechanism to achieve this by invoking a massive scalar field in the bulk space-time neglecting the back-reaction. In this work, we examine the possibility of stabilizing the modulus without bringing about any external scalar field. We show that instead of flat 3-branes as considered in Randall–Sundrum (RS) warped braneworld model, if one considers a more generalized version of warped geometry with de Sitter 3-brane, then the brane vacuum energy automatically leads to a modulus potential with a metastable minimum. Our result further reveals that in this scenario the gauge hierarchy problem can also be resolved for an appropriate choice of the brane’s cosmological constant.

Fermions in five-dimensional brane world models

In the present paper the fermion fields, living in the background of five-dimensional warped brane world models with compact extra dimension, are thoroughly examined. The Kaluza-Klein decomposition and isolation of the physical degrees of freedom is performed for those five-dimensional fermion field Lagrangians, which admit such a decomposition to be performed in a mathematically consistent way and provide a physically reasonable four-dimensional effective theory. It is also shown that for the majority of five-dimensional fermion field Lagrangians there are no (at least rather obvious) ways to perform the Kaluza-Klein decomposition consistently. Moreover, in these cases one may expect the appearance of various pathologies in the four-dimensional effective theory. Among the cases, for which the Kaluza-Klein decomposition can be performed in a mathematically consistent way, the case, which reproduces the Standard Model by the zero Kaluza-Klein modes most closely regardless of the size of the extra dimension, is examined in detail in the background of the Randall-Sundrum model.

Some problems with reproducing the Standard Model fields and interactions in five-dimensional warped brane world models

In this paper we examine, from the purely theoretical point of view and in a model-independent way, the case, when matter, gauge and Higgs fields are allowed to propagate in the bulk of five-dimensional brane world models with compact extra dimension, and the Standard Model fields and their interactions are supposed to be reproduced by the corresponding zero Kaluza–Klein modes. An unexpected result is that in order to avoid possible pathological behavior in the fermion sector, it is necessary to impose constraints on the fermion field Lagrangian. In the case when the fermion zero modes are supposed to be localized at one of the branes, these constraints imply an additional relation between the vacuum profile of the Higgs field and the form of the background metric. Moreover, this relation between the vacuum profile of the Higgs field and the form of the background metric results in the exact reproduction of the gauge boson and fermion sectors of the Standard Model by the corresponding zero mode four-dimensional effective theory in all the physically relevant cases, allowed by the absence of pathologies. Meanwhile, deviations from these conditions can lead either back to pathological behavior in the fermion sector or to a variance between the resulting zero mode four-dimensional effective theory and the Standard Model, which, depending on the model at hand, may, in principle, result in constraints putting the theory out of the reach of the present day experiments.

Induced dark energy in a warped braneworld and accelerating universe

In the six-dimensional (6D) Einstein gravity with a negative cosmological constant, we determine the structure of warped spacetimes bounded by 4-branes. We find an accelerating Universe solution with the induced dark energy, from the 4-brane obtained by orbifolding an external space, and suggest a possibility of addressing problems related to the cosmological constant.

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 $$\varLambda $$ of the AdS $$_{n}$$ spacetime is not equal to the naked one $$\varLambda _0$$ 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.

Vacuum force for a massive scalar field in a multiply warped braneworld

We determine the finite temperature Casimir force for a scalar massive field for a pair of parallel plates in a 6D non-factorizable geometry. In this contribution we use the Green's function method to determine the Casimir force. It can be expressed in terms of two four-dimensional Casimir force contributions: one for the zero mode and the other for a tower of massive modes associated with the extra dimensions. An uncertainty band of 10% around the theoretical standard 4D Casimir force was set up, by limiting the effective 4D Casimir force within such band yields the bound k/rz ≫ 1.97 × 106 TeV.

Time evolution of a warped cosmic string

The time evolution of a self-gravitating U(1) cosmic string on a warped five-dimensional (5D) axially symmetric spacetime is numerically investigated. Although cosmic strings are theoretically predicted in four-dimensional (4D) general relativistic models, there is still no observational evidence of their existence. From recent observations of the cosmic microwave background (CMB), it is concluded that these cosmic strings cannot provide a satisfactory explanation for the bulk of density perturbations. They even could not survive inflation. It is conjectured that only in a 5D warped braneworld model there will be observable imprint of these so-called cosmic superstrings on the induced effective 4D brane metric for values of the symmetry breaking scale larger than the grand unified theory (GUT) values. The warp factor makes these strings consistent with the predicted mass per unit length on the brane. However, in a time-dependent setting, it seems that there is a wavelike energy–momentum transfer to infinity on the brane, a high-energy braneworld behavior. This in contrast to earlier results in approximation models. Evidence of this information from the bulk geometry could be found in the gravitational cosmic background radiation via gravitational wave energy–momentum affecting the brane evolution. Fluctuations of the brane when there is a U(1) gauge field present, are comparable with the proposed brane tension fluctuations, or branons, whose relic abundance can be a dark matter candidate. We briefly made a connection with the critical behavior at the threshold of black hole formation found by Choptuik several decades ago in self-gravitating time-dependent scalar field models. The critical distinction between dispersion of the scalar waves and singular behavior fade away when a time-dependent warp factor is present.

Cosmology in multiply warped braneworld scenario

Hubble expansion in warped braneworld model is addressed in the presence of more than one warped extra dimensions. Some distinct phenomenological signatures of such model has already been discussed in the context of collider-based experiments as well as to explain the fermion mass hierarchy in the Standard Model of elementary particles. In this paper, we explore some cosmological implications of such a model. It is shown that while the expansion depends on all the moduli, an exponential nature of the expansion of the scale factor emerges as a generic feature which is independent of the number of extra dimensions but depends only on the bulk cosmological constant and brane pressure. A generalized expression for the effective 3-brane cosmological constant in such model has been derived. This generalizes the well-known fine tuning/detuning between the bulk cosmological constant and brane tension to obtain the desired cosmological constant on the brane. The warped factor corresponding to the higher-dimensional cosmological scenario is determined and the issue of gauge hierarchy problem is discussed.

On Closed Timelike Curves and Warped Brane World Models

At first glance, it seems possible to construct in general relativity theory causality violating solutions. The most striking one is the Gott spacetime. Two cosmic strings, approaching each other with high velocity, could produce closed timelike curves. It was quickly recognized that this solution violates physical boundary conditions. The effective one particle generator becomes hyperbolic, so the center of mass is tachyonic. On a 5-dimensional warped spacetime, it seems possible to get an elliptic generator, so no obstruction is encountered and the velocity of the center of mass of the effective particle has an overlap with the Gott region. So a CTC could, in principle, be constructed. However, from the effective 4D field equations on the brane, which are influenced by the projection of the bulk Weyl tensor on the brane, it follows that no asymptotic conical space time is found, so no angle deficit as in the 4D counterpart model. This could also explain why we do not observe cosmic strings.

Gauge and moduli hierarchy in a multiply warped braneworld scenario

Discovery of Higgs-like boson near the mass scale ∼126 Gev generates renewed interest to the gauge hierarchy problem in the standard model related to the stabilisation of the Higgs mass within Tev scale without any unnatural fine tuning. One of the successful attempts to resolve this problem has been the Randall–Sundrum warped geometry model. Subsequently this 5-dimensional model was extended to a doubly warped 6-dimensional (or higher) model which can offer a geometric explanation of the fermion mass hierarchy in the standard model of elementary particles (D. Choudhury and S. SenGupta, 2007 [1]). In an attempt to address the dark energy issue, we in this work extend such 6-dimensional warped braneworld model to include non-flat 3-branes at the orbifold fixed points such that a small but non-vanishing brane cosmological constant is induced in our observable brane. We show that the requirements of a Planck to Tev scale warping along with a vanishingly small but non-zero cosmological constant on the visible brane with non-hierarchical moduli, each with scale close to Planck length, lead to a scenario where the 3-branes can have energy scales either close to Tev or close to Planck scale. Such a scenario can address both the gauge hierarchy as well as fermion mass hierarchy problem in standard model without introducing hierarchical scales between the two moduli. Thus simultaneous resolutions to the gauge hierarchy problem, fermion mass hierarchy problem and non-hierarchical moduli problem are closely linked with the near flatness condition of our universe.

Matter–gravity interaction in a multiply warped braneworld

The role of a bulk graviton in predicting the signature of extra dimensions through collider-based experiments is explored in the context of a multiply warped spacetime. In particular it is shown that in a doubly warped braneworld model, the presence of the sixth dimension results in enhancement of concentration of graviton Kaluza–Klein (KK) modes compared to that obtained in the usual 5D Randall–Sundrum model. Also, the couplings of these massive graviton KK modes with the matter fields on the visible brane turn out to be appreciably larger than that in the corresponding 5D model. The significance of these results are discussed in the context of KK graviton search at the Large Hadron Collider (LHC).