Radion Field Research Articles

Effective Lagrangian and stability analysis in warped space

In the warped space model, the inter-brane distance can be stabilized by the Goldberger-Wise mechanism. Of particular importance, the stabilization potential calls for a proper identification of the dynamical degree of freedom. In this paper, we provided a complete calculation of the effective Lagrangian till the quadratic order that is generic for the Randall-Sundrum model and its N-brane (N ≥ 4) extensions. By applying the variation principle to a specific perturbation field, we derived the equations of motion and orthogonal conditions for decoupling the graviton. This approach is demonstrated to be equivalent to the analysis using the linearized Einstein equation. Our derivation clarifies that in the N-brane set up, just one degree of freedom for the radion field is dynamical, with the other modes eliminated by the gauge fixings. Thus we can directly generalize the GW stabilization to the N-brane model in a way similar to the RS1 scenario.

Radion dynamics, heavy Kaluza–Klein resonances and gravitational waves

In this paper, we study the confinement/deconfinement phase transition of the radion field in a warped model with a polynomial bulk potential. The backreaction of the radion on the metric is taken into account by using the superpotential formalism, while the radion effective potential is obtained from a novel formulation which can incorporate the backreaction. The phase transition leads to a stochastic gravitational wave background that depends on the energy scale of the first Kaluza–Klein resonance, [Formula: see text]. This work completes previous studies in the following aspects: (i) we detail the evaluation of the radion spectrum; (ii) we report on the mismatches between the thick wall approximation and the numerical bounce solution; (iii) we include a suppression factor in the spectrum of sound waves accounting for their finite lifetime; and (iv) we update the bound on [Formula: see text] in view of the O3 LIGO and Virgo data. We find that the forthcoming gravitational wave interferometers can probe scenarios where [Formula: see text], while the O3-run bounds rule out warped models with [Formula: see text] exhibiting an extremely strong confinement/deconfinement phase transition.

Radion dynamics in the multibrane Randall-Sundrum model

The radion equilibrium in the Randall-Sundrum (RS) model is guaranteed by the backreaction of a bulk scalar field. In this paper we study an extended scenario, where an intermediate brane exists in addition to the two branes at the fixed points, due to the discontinuity of bulk cosmology constants in two spatial regions. We conducted a complete analysis of the linearized Einstein's equations after applying the Goldberger-Wise mechanism. Our result elucidates that in the presence of nonfixed point branes under the rigid assumption, a unique radion field is conjectured as legitimate in the RS metric perturbation. The cosmological expansion in this setup is briefly discussed.

Critical analysis of modulus stabilization in a higher dimensional F(R) gravity

An exact solution for the bulk 5-dimensional geometry is derived for F(R) gravity with non-flat de-Sitter 3-branes located at the $M_4 \times Z_2$ orbifold boundaries. The corresponding form of F(R) that leads to such an exact solution of the bulk metric is derived which turns out to have all positive integer powers of R.In such a scenario the stability issue of the modulus (radion field) is analyzed critically for different curvature epochs in both Einstein and Jordan frames. The radion in the effective 4-d theory exhibits a phantom epoch making this model viable for a non-singular bounce. Simultaneous resolution of the gauge hierarchy problem is exhibited through the resulting stable vaue of the radion field in the effective $3+1$ dimensional theory.

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.

Nonlinear radion interactions

We consider the Randall–Sundrum model with two branes in which the fields of the Standard Model are localized on the brane with negative tension and the gravitational field and an additional stabilizing scalar Goldberg–Wise field propagate in the space between the branes. We construct a Lagrangian for scalar fluctuations of the gravitational and scalar fields against the background solution. We obtain an effective four-dimensional Lagrangian describing nonlinear self-coupling terms of the scalar radion field in a polynomial approximation up to the fourth order and also nonlinear terms of the coupling of the radion and Standard Model fields. We estimate possible values of the self-coupling constant.

Gravitational imprints from heavy Kaluza-Klein resonances

We systematically study the holographic phase transition of the radion field in a five-dimensional warped model which includes a scalar potential with a power-like behavior. We consider Kaluza-Klein (KK) resonances with masses $m_{\rm KK}$ at the TeV scale or beyond. The backreaction of the radion field on the gravitational metric is taken into account by using the superpotential formalism. The confinement/deconfinement first order phase transition leads to a gravitational wave stochastic background which mainly depends on the scale $m_{\rm KK}$ and the number of colors, $N$, in the dual theory. Its power spectrum peaks at a frequency that depends on the amount of tuning required in the electroweak sector. It turns out that the present and forthcoming gravitational wave observatories can probe scenarios where the KK resonances are very heavy. Current aLIGO data already rule out vector boson KK resonances with masses in the interval $m_{\rm KK}\sim(1 - 10) \times 10^5$ TeV. Future gravitational experiments will be sensitive to resonances with masses $m_{\rm KK}\lesssim 10^5$ TeV (LISA), $10^8$ TeV (aLIGO Design) and $10^9$ TeV (ET). Finally, we also find that the Big Bang Nucleosynthesis bound in the frequency spectrum turns into a lower bound for the nucleation temperature as $T_n \gtrsim 10^{-4}\sqrt{N} \,m_{\rm KK}$.

Geometries with mismatched branes

We study Randall-Sundrum two brane setups with mismatched brane tensions. For the vacuum solutions, boundary conditions demand that the induced metric on each of the branes is either de Sitter, Anti-de Sitter, or Minkowski. For incompatible boundary conditions, the bulk metric is necessarily time-dependent. This introduces a new class of time-dependent solutions with the potential to address cosmological issues and provide alternatives to conventional inflationary (or contracting) scenarios. We take a first step in this paper toward such solutions. One important finding is that the resulting solutions can be very succinctly described in terms of an effective action involving only the induced metric on either one of the branes and the radion field. But the full geometry cannot necessarily be simply described with a single coordinate patch. We concentrate here on the time- dependent solutions but argue that supplemented with a brane stabilization mechanism one can potentially construct interesting cosmological models this way. This is true both with and without a brane stabilization mechanism.

The Boundaries of KKLT

AbstractWe consider the conundrum of generating de Sitter space from higher‐dimensional geometry, with particular attention to KKLT‐type constructions[3] and their 5d implications. We show that even in the probe approximation with small , a consistent higher‐dimensional solution requires a deformation of a modulus field playing the role of a Goldberger‐Wise stabilizing field in Randall‐Sundrum type geometries that occurs through a shift in a the throat length. We identify the light radion field that sets the length of the throat, whose origin is the dynamical conifold deformation parameter. By analyzing the theory as a 5d model of mismatched branes in AdS5 space with a GW stabilization mechanism, we show how energy (and supersymmetry breaking) is transferred to both the IR and UV regions of the throat to generate a consistent 4d de Sitter sliced geometry. This should help resolve some of the recent apparent paradoxes in explicit higher‐dimensional constructions. Moreover, the radion gives insight into the potential for the previously identified “conifold instability”. We argue that this instability would be a destabilization of the potential for the radion in KKLT, which can occur when the perturbation is too large. If indeed is too small, the radion would enter on its runaway direction and the conifold deformation would shrink to zero size. It is difficult to satisfy the required bound and a) maintain a hierarchy in the simpler CY manifolds and b) complete the cosmological phase transition into the stabilized throat, We also discuss the implications of this type of setup for supersymmetry breaking, and how multiple throats can introduce hierarchies of supersymmetry breaking masses, even in an anomaly‐mediated scenario. In an appendix we consider general compactification constraints.

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.

Nonlinear interactions of the radion field

We study the Randall-Sundrum model with two branes. The Standard Model fields are localized on the brane with a negative tension, the gravitational field and scalar Goldberg-Wise field propagate in the multidimensional bulk. For this model we construct the Lagrangian for the scalar fluctuations of the gravitational and scalar fields above a background solution. We obtain an effective four-dimensional Lagrangian, which contains nonlinear self-interaction terms of the radion field up to the fourth order and nonlinear interactions of the radion and the Standard Model fields.

Radion stabilization in higher curvature warped spacetime

We consider a five dimensional AdS spacetime in presence of higher curvature term like F(R) = R + alpha R^2 in the bulk. In this model, we examine the possibility of modulus stabilization from the scalar degrees of freedom of higher curvature gravity free of ghosts. Our result reveals that the model stabilizes itself and the mechanism of modulus stabilization can be argued from a geometric point of view. We determine the region of the parametric space for which the modulus (or radion) can to be stabilized. We also show how the mass and coupling parameters of radion field are modified due to higher curvature term leading to modifications of its phenomenological implications on the visible 3-brane.

Inflationary scenario from higher curvature warped spacetime

We consider a five dimensional warped spacetime, in presence of the higher curvature term like F(R) = R + alpha R^2 in the bulk, in the context of the two-brane model. Our universe is identified with the TeV scale brane and emerges as a four dimensional effective theory. From the perspective of this effective theory, we examine the possibility of “inflationary scenario” by considering the on-brane metric ansatz as an FRW one. Our results reveal that the higher curvature term in the five dimensional bulk spacetime generates a potential term for the radion field. Due to the presence of radion potential, the very early universe undergoes a stage of accelerated expansion and, moreover, the accelerating period of the universe terminates in a finite time. We also find the spectral index of curvature perturbation (n_s) and the tensor to scalar ratio (r) in the present context, which match with the observational results based on the observations of Planck (Astron. Astrophys. 594, A20, 2016).

Gravity stabilizes itself

We show that a possible resolution to the stabilization of an extra spatial dimension (radion) can be obtained solely in the context of gravitational dynamics itself without the necessity of introducing any external stabilizing field. In this scenario the stabilized value of the radion field gets determined in terms of the parameters appearing in the higher curvature gravitational action. Furthermore, the mass of the radion field and its coupling to the standard model fields are found to be in the weak scale implying possible signatures in the TeV scale colliders. Some resulting implications are also discussed.

Higgs-radion phenomenology in stabilized RS models

An important general prediction of stabilized brane world models is the existence of a bulk scalar radion field, whose lowest Kaluza-Klein (KK) mode is the scalar particle called the radion. This field comes from the fluctuations of the metric in the extra dimension and the radion mass can be smaller than that of all the massive KK modes of the other particles propagating in the multidimensional bulk. Due to its origin, the radion and its KK tower couple to the trace of the energy-momentum tensor of the Standard Model. These fields have the same quantum numbers as the neutral Higgs field and can mix with the latter, if they are coupled. We present a short review of some aspects of Higgs-radion phenomenology in stabilized brane-world models. In particular, we discuss the possibility of explaining the 750 GeV excess by the production of a radion-dominated state.

Can extra dimensional effects allow wormholes without exotic matter?

We explore the existence of Lorentzian wormholes in the context of an effective on-brane, scalar-tensor theory of gravity. In such theories, the timelike convergence condition, which is always violated for wormholes, has contributions, via the field equations, from on-brane matter as well as from an effective geometric stress energy generated by a bulk-induced radion field. It is shown that, for a class of wormholes, the required on-brane matter, as seen by an on-brane observer in the Jordan frame, is not exotic and does not violate the Weak Energy Condition. The presence of the effective geometric stress energy in addition to on-brane matter is largely responsible for creating this intriguing possibility. Thus, if such wormholes are ever found to exist in the Universe, they would clearly provide pointers towards the existence of a warped extra dimension as proposed in the two-brane model of Randall and Sundrum.

Metric factorizability and equivalence of brane world models with Brans-Dicke theory

In the standard brane world models, the bulk metric ansatz is usually assumed to be factorizable in brane and bulk coordinates. However, it is not self-evident that it is always possible to factorize the bulk metric. Using the gradient expansion scheme, which involves the expansion of bulk quantities in terms of the brane-to-bulk curvature ratio as a perturbative parameter, we explicitly show that metric factorizability is a valid assumption up to second order in the perturbative expansion. We also argue from our result that the same should be true for all orders in the perturbation scheme. We further establish that the nonlocal terms present in the bulk gravitational field equation can be replaced by the radion field; the effective action on the brane thereby obtained resembles the Brans-Dicke theory of gravity.

Casimir dark energy, stabilization of the extra dimensions and Gauss–Bonnet term

Casimir dark energy model in five-dimensional and six-dimensional spacetime including non-relativistic matter and Gauss-Bonnet term is investigated. The Casimir energy can play the role of dark energy to drive the late-time acceleration of the universe while the radius of the extra dimensions can be stabilized. The qualitative analysis in radion picture in four-dimensional spacetime shows that the contribution from Gauss-Bonnet term will effectively slow down the radion field at the beginning time. Therefore, the radion field does not pass minimum point of the effective potential before the minimum of the potential exists. This leads to the stabilizing mechanism of the extra dimensions eventually.

Higgs boson-radion similarity in production processes involving off-shell fermions

The appearance of the radion field, which is associated with the spin-0 metric fluctuations combined in some manner with the scalar stabilizing field, and of the radion, the corresponding lowest Kaluza-Klein (KK) mode, is a generic prediction of stabilized brane world models. In such models the radion plays the role of the dilaton, and its mass may be somewhat smaller than that of all the KK modes of other particles propagating in the multidimensional bulk. Due to its origin, the radion couples to the trace of the energy-momentum tensor of the Standard Model, the interaction Lagrangian of the radion and the Standard Model fermions being similar to that of the SM Higgs-fermion interactions except for additional terms, which come into play only in the case of off-shell fermions. In the present paper it is shown that all the contributions to perturbative amplitudes of physical processes due to these additional terms are canceled out for both massless and massive off-shell fermions. Thus the additional fermion-radion terms in the interaction Lagrangian do not alter any production and decay properties of the radion compared to those of the Higgs boson.

Radion cosmology and stabilization

We solve the Einstein's equation in five-dimensional spacetime for Randall Sundrum Brane world model with time dependent radion field to study variation of brane scale factor with time. We have shown that as radion field decreases with time compactifying the extra dimension, the scale factor increases exponentially with time leading to inflationary scenario. We have also proposed a time dependent generalization of Goldberger-Wise moduli stabilization mechanism to explain the time evolution of the radion field to reach a stable value after which the scale factor on the brane exits from inflationary expansion.