Warped Geometry Research Articles

Inflation in warped geometries

We argue that brane anti-brane inflation in string theory de-Sitter vacua of Kachru–Kallosh–Linde–Trivedi (KKLT) is captured by the dynamics of a D3-brane probe in the local KKLT model constructed in hep-th/0203041. This provides a framework to study in a controllable way corrections to the inflationary slow roll parameter η due to conformal symmetry breaking in a warped geometry throat. We compute the leading correction to η for the inflation in the Klebanov–Tseytlin throat geometry. We find that in certain regime this correction tends to decrease η. Computations in a different regime suggest however that it is unlikely that η⪡1 can be achieved with the D3-brane throat inflation.

Braneworld dynamics with the BRANECODE

We give a full nonlinear numerical treatment of time-dependent 5d braneworld geometry, which is determined self-consistently by potentials for the scalar field in the bulk and at two orbifold branes, supplemented by boundary conditions at the branes. We describe the BraneCode, an algorithm which we designed to solve the dynamical equations numerically. We applied the BraneCode to braneworld models and found several novel phenomena of the brane dynamics. Starting with static warped geometry with de Sitter branes, we found numerically that this configuration is often unstable due to a tachyonic mass of the radion during inflation. If the model admits other static configurations with lower values of de Sitter curvature, this effect causes a violent re-structuring towards them, flattening the branes, which appears as a lowering of the 4d effective cosmological constant. Braneworld dynamics can often lead to brane collisions. We found that in the presence of the bulk scalar field, the 5d geometry between colliding branes approaches a universal, homogeneous, anisotropic strong gravity Kasner-like asymptotic, irrespective of the bulk/brane potentials. The Kasner indices of the brane directions are equal to each other but different from that of the extra dimension.

Stabilization of the Hierarchy in Brane-World Scenarios

We consider a class of warped brane models with topology M4 × Σ × S1/Z2, where Σ is a D2-dimensional compact manifold, and two branes are placed at the orbifold fixed points. In a scenario where supersymmetry is broken not far below the cutoff scale, the hierarchy between the electroweak and the Planck scales is generated by a combination of the redshift and the large volume effects. We evaluate the effective potential induced by bulk scalar fields in these models and show that it can stabilize the moduli and the hierarchy without fine-tuning, provided that the internal space Σ is flat. We also comment on the relation between these models and the five-dimensional scalar-tensor models that describe them classically when the compactification scale is small.

Can inflating braneworlds be stabilized?

We investigate scalar perturbations from inflation in braneworld cosmologies with extra dimensions. For this we calculate scalar metric fluctuations around five dimensional warped geometry with four dimensional de Sitter slices. The background metric is determined self-consistently by the (arbitrary) bulk scalar field potential, supplemented by the boundary conditions at both orbifold branes. Assuming that the inflating branes are stabilized (by the brane scalar field potentials), we estimate the lowest eigenvalue of the scalar fluctuations - the radion mass. In the limit of flat branes, we reproduce well known estimates of the positive radion mass for stabilized branes. Surprisingly, however, we found that for de Sitter (inflating) branes the square of the radion mass is typically negative, which leads to a strong tachyonic instability. Thus, parameters of stabilized inflating braneworlds must be constrained to avoid this tachyonic instability. Instability of "stabilized" de Sitter branes is confirmed by the BraneCode numerical calculations in the accompanying paper hep-th/0309001. If the model's parameters are such that the radion mass is smaller than the Hubble parameter, we encounter a new mechanism of generation of primordial scalar fluctuations, which have a scale free spectrum and acceptable amplitude.

Precision electroweak data and the mixed radion–Higgs sector of warped extra dimensions

We derive the Lagrangian and Feynman rules up to bilinear scalar fields for the mixed Higgs-radion eigenstates interacting with Standard Model particles confined to a 3-brane in Randall-Sundrum warped geometry. We use the results to compute precision electroweak observables and compare theory predictions with experiment. We characterize the interesting regions of parameter space that simultaneously enable a very heavy Higgs mass and a very heavy radion mass, both masses being well above the putative Higgs boson mass limit in the Standard Model derived from the constraints of precision electroweak observables. For parameters consistent with the precision constraints the Higgs boson physical eigenstate is typically detectable, but its properties may be difficult to study at the Large Hadron Collider. In contrast, masses and couplings are allowed for the physical radion eigenstate that make it unobservable at the LHC. A Linear Collider will significantly improve our ability to study the Higgs eigenstate, and will typically allow detection of the radion eigenstate if it is within the machine's kinematical reach.

Realistic D-Brane Models on Warped Throats: Fluxes, Hierarchies and Moduli Stabilization

We describe the construction of string theory models with semirealistic spectrum in a sector of (anti) D3-branes located at an orbifold singularity at the bottom of a highly warped throat geometry, which is a generalisation of the Klebanov-Strassler deformed conifold. These models realise the Randall-Sundrum proposal to naturally generate the Planck/electroweak hierarchy in a concrete string theory embedding, and yielding interesting chiral open string spectra. We describe examples with Standard Model gauge group (or left-right symmetric extensions) and three families of SM fermions, with correct quantum numbers including hypercharge. The dilaton and complex structure moduli of the geometry are stabilised by the 3-form fluxes required to build the throat. We describe diverse issues concerning the stabilisation of geometric Kahler moduli, like blow-up modes of the orbifold singularities, via D term potentials and gauge theory non-perturbative effects, like gaugino condensation. This local geometry, once embedded in a full compactification, could give rise to models with all moduli stabilised, and with the potential to lead to de Sitter vacua. Issues of gauge unification, proton stability, supersymmetry breaking and Yukawa couplings are also discussed.

Inter-brane interactions incompact spaces and brane inflation

It has been pointed out that brane–anti-brane inflation without warped geometry is not viable due to compactification effects (in the simplified scenario where the inflaton is decoupled fromthe compactification moduli). We show that the inflationaryscenario with branes at a small angle in this simplifiedscenario remains viable. We also point out thatbrane–anti-brane inflation may still be viable under somespecial conditions. We also discuss a way to treat potentials incompact spaces that should be useful in the analysis of morerealistic brane inflationary scenarios.

Brane structure from a scalar field in warped spacetime

We deal with a scalar field coupled to gravity in five dimensionsin a warped geometry. We investigate models described by potentialsthat drive the system to support thick brane solutions that engenderinternal structure. We find analytical expressions for the brane solutions,and we show that they are all linearly stable.

Seesaw mechanism in warped geometry

We show how the seesaw mechanism for neutrino masses can be realized within a five-dimensional (5D) warped geometry framework. Intermediate scale standard model (SM) singlet neutrino masses, needed to explain the atmospheric and solar neutrino oscillations, are shown to be proportional to MPlexp((2c−1)πkR), where c denotes the coefficient of the 5D Dirac mass term for the singlet neutrino which also has a Planck scale Majorana mass localized on the Planck-brane, and kR≈11 in order to resolve the gauge hierarchy problem. The case with a bulk 5D Majorana mass term for the singlet neutrino is briefly discussed.

Black Brane World from Gravitating Half -lump

We study O($N+1$) nonlinear $\sigma$-model in $(p+1+N)$-dimensional curved spacetime with negative cosmological constant, and find a new $\sigma$-lump solution with half-integer winding and divergent energy. When the spatial structure of $N$ extra-dimensions is determined by this global defect, a black $\sigma p$-brane surrounded by the degenerated horizon is formed and its near-horizon geometry is identified as a warp geometry of cigar type.

The Shifted Warped Normal Model for Mortality

The Shifted Warped Normal Model for Mortality

CP violation in models with TeV-scale SUSY breaking

We estimate contributions of the goldstino supermultiplet to the electric dipole moment (EDM) in the case that the SUSY breaking scale ΛS is of order the TeV scale. We found that such contributions can saturate the experimental bound if ΛS is close to the soft mass scale. We also discuss EDM in the gaugino-mediated scenario on the warped geometry as an example of models with the TeV-scale SUSY breaking.

Einstein spaces in warped geometries in five dimensions

We investigate five dimensional Einstein spaces in warped geometries from the point of view of the four dimensional physically relevant Robertson-Walker-Friedman cosmological metric and the Schwarzschild metric. We show that a four-dimensional cosmology with a closed spacelike section and a cosmological constant can be imbedded into five-dimensional flat space-time.

Une asymétrie dans les tourbillons cosmiques

Amongst all objects in the universe, spiral galaxies resemble what could be called cosmic storms. Despite their apparently regular shapes, these huge rotating structures are sometimes subject to strange asymmetries. Fifty years ago, observers found that the outer parts of our galactic disk were not flat, but exhibited an asymmetric warp. Today, about half of the known galaxies are considered as warped, but no theory has been able to explain this phenomenon. Taking a look at this, we first introduce some general concepts about spiral and warped galaxies. Then, we explore the problem of the longevity of warped galaxies when the matter is distributed in a disk. We use a semi-analytic method to study the existence of stable periodic orbits in a warped analytic model. A N-body simulation provides information on the dynamical evolution of a warped galaxy.

A small cosmological constant and backreaction of non-finetuned parameters

We include the backreaction on the warped geometry induced by non-finetuned parameters in a two domain-wall set-up to obtain an exponentially small Cosmological Constant $\Lambda_4$. The mechanism to suppress the Cosmological Constant involves one classical fine-tuning as compared to an infinity of finetunings at the quantum level in standard D=4 field theory.

De Sitter vacua in string theory

We outline the construction of metastable de Sitter vacua of type IIB string theory. Our starting point is highly warped IIB compactifications with nontrivial NS and RR three-form fluxes. By incorporating known corrections to the superpotential from Euclidean D-brane instantons or gaugino condensation, one can make models with all moduli fixed, yielding a supersymmetric AdS vacuum. Inclusion of a small number of $\overline{\mathrm{D}3}$-branes in the resulting warped geometry allows one to uplift the AdS minimum and make it a metastable de Sitter ground state. The lifetime of our metastable de Sitter vacua is much greater than the cosmological time scale of ${10}^{10}\mathrm{yr}.$ We also prove, under certain conditions, that the lifetime of dS space in string theory will always be shorter than the recurrence time.

Flavor violation and warped geometry

Extra dimensions have interesting consequences for flavor physics. We consider a setup where the standard model fermions and gauge fields reside in the bulk of a warped extra dimension. Fermion masses and mixings are explained by flavor dependent fermion locations, without relying on hierarchical Yukawa couplings. We discuss various flavor violating processes induced by (Kaluza–Klein) gauge boson exchange and non-renormalizable operators. Experimental constraints are satisfied with a Kaluza–Klein scale of about 10 TeV. Some processes, such as muon–electron conversion, are within reach of next generation experiments.

Neutrino oscillations, rare decays and warped geometry

We discuss how the solar and atmospheric neutrino anomalies can be satisfactorily resolved via neutrino oscillations in a five-dimensional framework with warped geometry. In one particularly significant example, no new fields such as singlet (right-handed) neutrinos have to be introduced. We also consider rare processes including proton and neutrinoless double beta decays. The Kaluza–Klein excitations of the standard model particles are predicted to possess masses in the 10 TeV range.

Cosmological constant, gauge hierarchy, and warped geometry

It is suggested that the mechanism responsible for the resolution of the gauge hierarchy problem within the warped geometry framework can be generalized to provide a new explanation of the extremely tiny vacuum energy density rho_V suggested by recent observations. We illustrate the mechanism with some 5D examples in which the true vacuum energy is assumed to vanish, and rho_V is associated with a false vacuum energy such that rho_V^{1/4} ~ TeV^2/M_{Pl} ~ 10^{-3} eV, where M_{Pl} denotes the reduced Planck mass. We also consider a quintessence-like solution to the dark energy problem.

Lensed density perturbations in braneworlds: Towards an alternative to perturbations from inflation

We consider a scenario in which our observable universe is a 3-dimensional surface (3-brane) living in extra dimensions with a warped geometry. We show that ``lensed'' density perturbations from other branes serve as possible seeds for structure formation on our observable brane (without inflation), and, in addition, provide constraints on braneworld scenarios with warped bulk geometry. Due to the warped bulk metric, any perturbation generated on one brane (or in the bulk matter) appears to an observer on a second brane to have a significantly different amplitude. We analyze lensed perturbations in the Randall-Sundrum type scenarios and the ``shortcut metric'' scenarios. For Lorentz violating metrics in the bulk, we find the attractive possibility that large density fluctuations that are causally produced elsewhere can lead to small density fluctuations on our brane on superhorizon (acausal) length scales, as required by structure formation. Our most interesting result is that the ``shortcut metrics'' in which geodesics traverse the extra dimensions provide an alternative to inflation with two important features: a possible solution to the horizon problem and a mechanism to generate perturbations necessary for structure formation.