Braneworld Model Research Articles

Data-driven and almost model-independent reconstruction of modified gravity

In this paper, a modified factor μ, which characterizes modified gravity in the linear matter density perturbation theory, is reconstructed in a data-driven and almost model-independent way via Gaussian process by using currently available cosmic observations. Utilizing the Pantheon+ SNe Ia samples, the observed Hubble parameter H(z) and the redshift space distortion fσ 8(z) data points, one finds out a time varying μ at low redshifts. The reconstructed μ implies that more complicated modified gravity beyond the simplest general relativity and the Dvali-Gabadadze-Porrati braneworld model is required.

Localization of abelian gauge fields with Stueckelberg-like geometrical coupling on f(T, B)-thick brane

In the context of f(T, B) modified teleparallel gravity, we investigate the influence of torsion scalar T and boundary term B on the confinement of both the gauge vector and Kalb–Ramond fields. Both fields require a suitable coupling in five-dimensional braneworld scenarios to yield a normalizable zero mode. We propose a Stueckelberg-like geometrical coupling that non-minimally couples the fields to the torsion scalar and boundary term. To set up our braneworld models, we use the first-order formalism in which two kinds of superpotential are taken: sine-Gordon and phi ^{4}-deformed. The geometrical coupling is used to produce a localized zero mode. Moreover, we analyze the massive spectrum for both fields and obtain possible resonant massive modes. Furthermore, we do not find tachyonic modes leading to a consistent thick brane.

Holographic time-dependent entanglement entropy in p-brane gas geometries

We study the time evolution of entanglement entropy in expanding universes with various matters. To describe expanding universes holographically, we take into account a braneworld moving in an asymptotic AdS space involving a uniform p-brane gas. In the braneworld model, an observer living in the braneworld detects the bulk motion of the braneworld as an expanding universe. We show that the entanglement entropy of expanding universes increases by the volume law in the early time and by the area law in the late time. We further consider the cosmological horizon, which is the border of the visible and invisible universe, and then investigate the time-dependent quantum entanglement between them across the cosmological horizon.

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.

How slowly can the early Universe expand?

When the expansion of the Universe is dominated by a perfect fluid with equation of state parameter $w$ and a sound speed ${c}_{s}$ satisfying $w={c}_{s}^{2}\ensuremath{\le}1$, the Hubble parameter $H$ and time $t$ satisfy the bound $Ht\ensuremath{\ge}1/3$. There has been recent interest in ``ultraslow'' expansion laws with $Ht<1/3$ (sometimes described as ``fast expanding'' models). We examine various models that can produce ultraslow expansion: scalar fields with negative potentials, barotropic fluids, braneworld models, or a loitering phase in the early Universe. Scalar field models and barotropic models for ultraslow expansion are unstable to evolution toward $w=1$ or $w\ensuremath{\rightarrow}\ensuremath{\infty}$ in the former case and $w\ensuremath{\rightarrow}\ensuremath{\infty}$ in the latter case. Braneworld models can yield ultraslow expansion but require an expansion law beyond the standard Friedman equation. Loitering early universe models can produce a quasistatic expansion phase in the early Universe but require an exotic negative-density component. These results suggest that appeals to an ultraslow expansion phase in the early Universe should be approached with some caution, although the loitering early universe may be worthy of further investigation. These results do not apply to ultraslow contracting models.

D-term inflation in braneworld models: Consistency with cosmic-string bounds and early-time Hubble tension resolving models

We revisit D-term inflation with the bounds of the cosmic string tension from gravitational wave observations and consider the possible deviation of the spectral index compared with the $\Lambda$CDM model in light of prerecombination resolutions of the Hubble tension. D-term inflation requires very small coupling constants under these constraints. We show that natural coupling constants ($g=\lambda=0.1$) can be achieved in the case of D-term inflation on the brane.

Thick brane models in generalized mimetic gravity

In this work, we investigate braneworld models in mimetic gravity, with the source field having generalized dynamics. We present the mathematical description necessary to study the generalized model and consider the first-order formalism to solve the equations of motion. We also investigate the linear stability of the gravitational sector to verify that the model is stable. In particular, we consider two specific situations where we were able to get exact solutions with a kink-like profile and calculate several important properties of the brane.

Gravity localization on intersecting thick braneworlds

The localization of gravity for ($5+1$)-dimensional intersecting thick braneworld models is thoroughly investigated. Departing from preliminary results for five independent proposals, from $I$ to $V$, gravity is shown to be localized in the brane. In particular, for models from $I$ to $III$, only the zero modes are analytically determined. On the other hand, for models $IV$ and $V$, massive modes are all obtained: a finite number of massive states is identified for model $IV$, while an infinite but discrete number of massive states bounded from below is exhibited by model $V$. Considering that the discreteness of the graviton modes implies that gravity does not propagate in the codimensions, the naked singularities of models $IV$ and $V$, at edges of space, are made harmless. To conclude, the phenomenological implications for sphere models, constructed out of models $III$ and $IV$, are also discussed. According to such an overall classification, if the internal space is a sphere, model $IV$ is shown to exhibit normalizable modes. More relevantly, for the sphere model assembled out of model $III$, the subtle property of reproducing a consistent Newtonian limit is identified.

Double holography in string theory

We develop the notion of double holography in Type IIB string theory realizations of braneworld models. The Type IIB setups are based on the holographic duals of 4d BCFTs comprising 4d mathcal{N} = 4 SYM on a half space coupled to 3d mathcal{N} = 4 SCFTs on the boundary. Based on the concrete BCFTs and their brane construction, we provide microscopic realizations of the intermediate holographic description, obtained by dualizing only the 3d degrees of freedom. Triggered by recent observations in bottom-up models, we discuss the causal structures in the full BCFT duals and intermediate descriptions. This confirms qualitative features found in the bottom-up models but suggests a refinement of their interpretation.

Self-tuning of the cosmological constant in brane-worlds with P(X,ϕ)

We revisit the idea of self-tuning the observed cosmological constant to a vanishing value and promote it to a selection criterion of brane-world models, in which our Universe is described by a 3-brane embedded in a 5d bulk. As a concrete setup, we consider a bulk scalar field ϕ described by a general Lagrangian P(X,ϕ) with X = -(∂ϕ)2/2. By requiring that the model enforces the 4d curvature of the maximally symmetric 3-brane world-volume to vanish independently of the 4d effective vacuum energy, only two possibilities remain: one with a canonical bulk kinetic term and the other with an unconventional bulk kinetic term similar to a Cuscuton field. Further demanding the absence of bulk singularity, the latter is selected as a unique possibility within the class of models. At the background level, the solution can accommodate any warp factor profile free from bulk singularity and with a finite effective 4d Planck mass. In a cosmological context, our solution would describe our (almost) flat Universe at late times, with a bulk warp factor profile expected to be determined by the evolution of the Universe before dilution of the matter fields by cosmic expansion. Eventually, a simple analysis is performed in the bulk showing no obvious instability around the background solution. A full stability analysis taking into account brane bending modes is nevertheless necessary and left for future work.

Majorana zero mode-soliton duality and in-gap and BIC bound states in modified Toda model coupled to fermion

A two-dimensional field theory of a fermion chirally coupled to Toda field plus a scalar self-coupling potential is considered. Using techniques of integrable systems we obtain analytical zero modes, in-gap states and bound states in the continuum (BIC) for topological configurations of the scalar field. Fermion-soliton duality mappings are uncovered for the bound state spectrum, which interpolates the weak and strong coupling sectors of the model and give rise to novel Thirring-like and multi-frequency sine-Gordon models, respectively. The non-perturbative effects of the back-reaction of the fermion bound states on the kink are studied and it is shown that the zero mode would catalyze the emergence of a new kink with lower topological charge and greater slope at the center, in the strong coupling limit of the model. For special topological charges and certain relative phases of the fermion components the kinks can host Majorana zero modes. The Noether, topological and a novel nonlocal charge densities satisfy a formula of the Atiyah-Patodi-Singer-type. Our results may find applications in several branches of non-linear physics, such as confinement in QCD2, braneworld models, high Tc superconductivity and topological quantum computation. We back up our results with numerical simulations for continuous families of topological sectors.

Relieving string tension by making baby universes in a dynamical string tension braneworld model

String tension fundamentally determines the properties of strings; yet its value is often assigned arbitrarily, creating a fine-tuning problem. We describe a mechanism for dynamically generating string tension in a flat or almost flat spacetime, using the ‘modified measures formalism’, which in turn naturally generates a new type of stringy braneworld scenario. Such a scenario allows strings to achieve near infinite tension confining the strings to two very close expanding surfaces, but the infinite tensions also threaten to distort the near-flat embedding spacetime through large back reactions. We argue that this danger can be neutralized via the creation of a baby universe — a growing region of embedding spacetime that divorces from the ambient embedding spacetime, while our universe is still a brane separating two nearly flat spacetimes. The avoidance of a minimum length and a maximum Hagedorn temperature in the context of dynamical string tension generation is also discussed.

New results for cuscuton multi-field brane

We investigate braneworld models in the presence of the several scalar fields with generalized dynamics. A new mechanism to control the internal structure of brane in modified gravity is used to induce changes in the models in the presence of cuscuton dynamics. Examples with two- and three-field are considered, and we have found that the inclusion of the cuscuton can significantly alter the profile of the brane, causing unique changes in the warp factor, energy density, stability potential and the corresponding zero mode.

Softly higher-derivative massive gravity

In this work, we study the higher-derivative massive gravity in D-dimensional space-time with the mass term arisen due to a 2-brane embedded in a 4D Minkowski spacetime. We consider the effect of a resonance mass term from the DGP braneworld model for the higher-derivative massive gravity. Moreover, we add the gravitational Chern–Simons and Ricci–Cotton terms to this model and evaluate the graviton propagator using a basis of Barnes–Rivers spin projectors. Using the obtained propagator, we proceed with discussing the consistency of the model, writing the dispersion relations, and analyzing causality and unitarity.

ΛCDM ∪ MOND

It has been demonstrated that the difference between the Renormalised Brane World (RBW) model andthe Lambda Cold Dark Matter (ΛCDM) model occurs only at sufficiently distant times. In thispaper, it is shown that for spherically symmetric situations an analog deviation between the RBWmodel and Newton's theory occurs at large distances. More precisely, this deviation of the RBWmodel is nothing other than the explanation of Milgrom's hypothesis and follows fromitself. Therefore, the results of this paper explains flat rotation curves of galaxies without dark matter.

Topological structures of event horizons along framed null Cartan curves in Minkowski space

In this work, we model two event horizons associated with a null Cartan curve as two lightlike hypersurfaces, respectively. We define a lightlike surface and a spacelike surface whose images coincide with the sets of critical values of two event horizons, and meanwhile we present two curves whose images coincide with the sets of critical values of these two surfaces, respectively. Using the singularity theory, we characterize the local topological structures of two event horizons, two surfaces and two curves at their singularities by means of two new invariants. Moreover, we also present a spacelike braneworld model along the particle as a spacelike surface in hyperbolic 3-space. An important fact shows that from the viewpoint of Legendrian dualities, this surface is [Formula: see text]-dual to the tangent trajectory [Formula: see text] of the null Cartan curve in Lorentz–Minkowski space-time. Meanwhile, we also consider a curve whose image is the set of critical values of this surface in hyperbolic 3-space. The third invariant of the null Cartan curve characterizes the singularities of the surface [Formula: see text] and the curve [Formula: see text] in hyperbolic 3-space. A result indicates that surface [Formula: see text] is locally diffeomorphic to the swallowtail [Formula: see text] or cuspidal edge [Formula: see text] and [Formula: see text] is locally diffeomorphic to the [Formula: see text]-cusp at certain a singular point. It is also shown that there exist deep relationships between the singularities of the surface [Formula: see text] and the curve [Formula: see text] and the order of contact between [Formula: see text] and elliptic quadric [Formula: see text] or the order of contact between [Formula: see text] and spacelike hyperplane [Formula: see text]. Finally, we present several examples to describe the main results.

Boltzmann and Tsallis statistical approaches to study quantum corrections at large distances and clustering of galaxies

Gravity is so different from other fundamental forces that it is now essentially treated as a nonfundamental force of entropic origin. Several good studies have been carried out in this direction. Quantum gravity is a theory which combines gravity well with quantum physics. However, there are still many impediments to our understanding, especially in the limits of extreme. The effects of quantum gravity start appearing on the scene at Planck length which is the smallest length in nature idealized so far. Although this study incorporates a model which is valid for potential energy corrections at small distances, we have also given a bold try to use it consistently for the corrections at very large distances as well. The model uses two techniques, namely, Boltzmann and Tsallis statistical approaches to explore the thermodynamics within the ambit of the braneworld model giving its further modified version. We have computed the partition function by using both Boltzmann and Tsallis statistical approaches and then used it to study the thermodynamics of the braneworld model. We have analyzed both analytically and graphically, the thermodynamic quantities like Helmholtz free energy and specific heat.

Brane cosmology with variable tension

We study brane-world models and demonstrate that such models do not admit self-similar solutions through the matter collineation approach. By introducing the hypothesis of variable brane tension, λ, we outline the new effective field equation (EFE) in the most simple case (symmetric embedding) under the assumption that the fundamental constants in five dimensions (5D) are constants. In this case, we find the exact form that each physical quantity may take in order that the EFE become invariant under scale transformations. By taking into account such assumptions, we find that in four dimensions the gravitational constant κ2 ∼ λ, while the cosmological constant Λ ∼ λ2 is always decreasing. These results are quite general and valid for any homogeneous self-similar metric. Nevetheless, the study of the EFE under scale symmetries suggests that ρ ∼ λ (as a functional relationship). This allows us to get a growing κ2 but, in this case, the fundamental constants in 5D must vary as well. We outline a toy model allowing such a possibility.

Shadows and observation intensity of black holes in the Randall–Sundrum brane world model * *Supported by the National Natural Science Fund of China (11775038, 12047564)

The shadow and observation intensity of a black hole surrounded by a thin spherical accretion in the Randall–Sundrum brane world model are investigated. The bulk metric depends on the tidal charge parameter, q, and deformation parameter, C. It reduces to the metric that possesses similar form with the Reissner–Nordström metric if . It is shown that the radius of the photon sphere of this black hole depends only on the tidal charge parameter. The radius of the photon sphere decreases with higher q. The observation intensity is mainly influenced by the tidal charge parameter, q, and the deformation parameter, C, is of secondary importance. In the optical observation, the black holes appear brighter with higher q or lower C.

Towards an accurate model of small-scale redshift-space distortions in modified gravity

ABSTRACT The coming generation of galaxy surveys will provide measurements of galaxy clustering with unprecedented accuracy and data size, which will allow us to test cosmological models at much higher precision than achievable previously. This means that we must have more accurate theoretical predictions to compare with future observational data. As a first step towards more accurate modelling of the redshift space distortions (RSD) of small-scale galaxy clustering in modified gravity (MG) cosmologies, we investigate the validity of the so-called Skew-T (ST) probability distribution function (PDF) of halo pairwise peculiar velocities in these models. We show that, combined with the streaming model of RSD, the ST PDF substantially improves the small-scale predictions by incorporating skewness and kurtosis, for both Λ cold dark matter (ΛCDM) and two leading MG models: f(R) gravity and the DGP braneworld model. The ST model reproduces the velocity PDF and redshift-space halo clustering measured from MG N-body simulations very well down to $\sim 5 \, h^{-1}\, \mathrm{Mpc}$. In particular, we investigate the enhancements of halo pairwise velocity moments with respect to ΛCDM for a larger range of MG variants than previous works, and present simple explanations to the behaviours observed. By performing a simple Fisher analysis, we find a significant increase in constraining power to detect modifications of General Relativity by introducing small-scale information in the RSD analyses.