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.     

Quantum Stabilization of Moduli in a Slice of AdS6 Compactified on S 1

We review the effective potential due to massive bulk scalar fields in higher-dimensional warped brane models found in Flachi et al. (Quantum stabilization of moduli in higher dimensional brane models, arXiv:hep-th/0301, 2003) specializing it to a slice of AdS₆ compactified on the circle. This model contains two moduli that parametrize the interbrane distance and the size of S ¹, or equivalently the positions of the two branes. Their values determine the Planck/EW hierarchy, in a combination of large volume and redshift effects. It is found that the observed hierarchy is compatible with both moduli stabilized by the Casimir forces without fine-tuning (except for the one needed to match the cosmological constant). This contrasts with the Randall—Sundrum model, where gauge fields in the bulk are needed.     

Localization of scalar fields on self-gravitating thick branes

The model of a domain wall (“thick” brane) in noncompact five-dimensional spacetime is considered with geometries of AdS ₅ type generated by self-interacting scalar matter. The scalar matter is composed of two fields with O(2) symmetric self interaction. One of them is mixed with gravity scalar modes and plays role of the brane formation mode (due to a kink background) and another one is of a Higgs-field type. The interplay between soft breaking of O(2) symmetry and gravity influence is thoroughly investigated around the critical point of spontaneous t symmetry breaking when the v.e.v. of the Higgs-type scalar field occurs. The possibility of (quasi)localization of scalar modes on such thick branes is examined.     

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.     

Hierarchy problem and the cosmological constant in a five-dimensional Brans-Dicke brane world model

We discuss a new solution, admitting the existence of dS ₄ branes, in five-dimensional Brans-Dicke theory. It is shown that, due to a special form of a bulk scalar field potential, for certain values of the model parameters the effective cosmological constant can be made small on the brane, where the hierarchy problem of gravitational interaction is solved. We also discuss new stabilization mechanism which is based on the use of auxiliary fields.     

The <Emphasis Type="Italic">A</Emphasis><Emphasis Type="Italic">d</Emphasis><Emphasis Type="Italic">S</Emphasis><Subscript>5</Subscript> Warp of Spatially Hyperbolic Universes,Spinless Modes and Spectra and the Corresponding Wheeler–DeWitt Schrödinger-Like Equation

In this paper, we consider an A d S ₅ bulk with k=?1? FRW branes, together with bosons test particles, evolving in the 5D hyperspace. In the first part, we compute the wave function of the scalar fields in the bulk and the allowed mass spectrum for physically relevant cases. Also, an important quantization law, connecting the mass spectrum of the bosons on the brane and the bulk mass parameter is written down. In the second part, in oder to develop a quantization model, we use the Wheeler-DeWitt equation and solve its Schrödinger-like form, obtaining the wave function of the Universe. The solutions describe a universe emerging out of nothing, without tunneling. Lastly, using a mixture of states, we emphasize a smooth universe, with neither Bangs nor Crunches.     

Hybrid Bloch brane

This work reports on models described by two real scalar fields coupled with gravity in the five-dimensional spacetime, with a warped geometry involving one infinite extra dimension. Through a mechanism that smoothly changes a thick brane into a hybrid brane, one investigates the appearance of hybrid branes hosting internal structure, characterized by the splitting on the energy density and the volcano potential, induced by the parameter which controls interactions between the two scalar fields. In particular, we investigate distinct symmetric and asymmetric hybrid brane scenarios.     

Brane worlds in collision

We obtain an exact solution of the supergravity equations of motion in which the four-dimensional observed Universe is one of a number of colliding D3 branes in a Calabi-Yau background. The collision results in the ten-dimensional spacetime splitting into disconnected regions, bounded by curvature singularities. However, near the D3 branes the metric remains static during and after the collision. We also obtain a general class of solutions representing p-brane collisions in arbitrary dimensions, including one in which the universe ends with the mutual annihilation of a positive-tension and a negative-tension 3 brane.     

Entropy of anisotropic universe and fractional branes

We obtain the entropy of a homogeneous anisotropic universe applicable, by assumption, to the fractional branes in the universe in the model of Chowdhury and Mathur. The entropy for the 3 or 4 charge fractional branes thus obtained is not of the expected form or E ². One way the expected form is realised is if p → ρ for the transverse directions and if the compact directions remain constant in size. These conditions are likely to be enforced by brane decay and annihilation, and by the S, T, U dualities. T duality is also likely to exclude high entropic cases, found in the examples, which arise due to the compact space contracting to zero size. Then the 4 charge fractional branes may indeed provide a detailed realisation of the maximum entropic principle we proposed recently to determine the number (3 + 1) of large spacetime dimensions.     

Two-Brane Randall-Sundrum Model in AdS 5 and dS 5

Two flat Randall-Sundrum three-branes are analyzed, at fixed mutual distance, in the case where each brane contains an ideal isotropic fluid. Both fluids are to begin with assumed to obey the equation of state p = ( – 1), where is a constant. Thereafter, we impose the condition that there is zero energy flux from the branes into the bulk, and assume that the tension on either brane is zero. It then follows that constant values of the fluid energies at the branes are obtained only if the value of is equal to zero (i.e., a vacuum fluid). The fluids on the branes are related: if one brane is a dS ₄ brane (the effective four-dimensional constant being positive), then the other brane is dS ₄ also, and if the fluid energy density on one brane is positive, the energy density on the other brane is larger in magnitude but negative. This is a non-acceptable result, which sheds some light on how far it is possible to give a physical interpretation of the two-brane scenario. Also, we discuss the graviton localization problem in the two-brane setting, generalizing prior works.     

Brane Formation and Cosmological Constraint on the Number of Extra Dimensions

Special relativity is generalized to extra dimensions and quantized energy levels of particles are obtained. By calculating the probability of particles' motion in extra dimensions at high temperature of the early universe, it is proposed that the branes may have not existed since the very beginning of the universe, but formed later. Meanwhile, before the formation, particles of the universe may have filled in the whole bulk, not just on the branes. This scenario differs from that in the standard big bang cosmology in which all particles are assumed to be in the 4D spacetime. So, in brane models, whether our universe began from a 4D big bang singularity is questionable. A cosmological constraint on the number of extra dimensions is also given which favors N ≥ 7.     

Phenomenology of a realistic accelerating universe using tracker fields

We present a realistic scenario of tracking of scalar fields with varying equation of state. The astrophysical constraints on the evolution of scalar fields in the physical universe are discussed. The nucleosynthesis and the galaxy formation constraints have been used to put limits on Ω_φ and estimate ɛ during cosmic evolution. Interpolation techniques have been applied to estimate ɛ ⋍0.772 at the present epoch. The epoch of transition from matter to quintessence dominated era and consequent onset of acceleration in cosmic expansion is calculated and taking the lower limit Θ _n ^/0 =0.2 as estimated from SN _e I _a data, it is shown that the supernova observations beyond redshift z=1 would reveal deceleration in cosmic expansion.     

Space-time compactification/decompactification transitions via lightlike branes

We consider Einstein-Maxwell-Kalb-Ramond gravity-matter system in bulk space-time interacting self-consistently with two (widely separated) codimension-one electrically charged lightlike branes. The lightlike brane dynamics is explicitly given by manifestly reparametrization invariant world-volume actions in two equivalent dual to each other formulations (Polyakov-type and Nambu-Goto-type ones) proposed in our previous work. We find an explicit solution of the pertinent Einstein-Maxwell-Kalb-Ramond-lightlike-brane equations of motion describing a “two-throat” wormhole-like space-time consisting of a “left” compactified Bertotti-Robinson universe connected to a “middle” non-compact Reissner-Nordström- de-Sitter space-time region, which in turn is connected to another “right” compactified Bertotti-Robinson universe. Each of the lightlike branes automatically occupies one of the “throats”, so that they dynamically induce a sequence of spontaneous space-time compactification/decompactification transitions.     

“Mass inflation” with lightlike branes

We discuss properties of a new class of p-brane models, describing intrinsically lightlike branes for any world-volume dimension, in various gravitational backgrounds of interest in the context of black hole physics. One of the characteristic features of these lightlike p-branes is that the brane tension appears as an additional nontrivial dynamical world-volume degree of freedom. Codimension one lightlike brane dynamics requires that bulk space with a bulk metric of spherically symmetric type must possess an event horizon which is automatically occupied by the lightlike brane while its tension evolves exponentially with time. The latter phenomenon is an analog of the well known “mass inflation” effect in black holes.      

Localization of matters on the bent brane in bulk

We investigate the possibility of localizing various matter fields on a bent AdS₄ (dS₄) thick brane in AdS₅. For spin 0 scalar field, we find a massless zero mode and an excited state which can be localized on the bent brane. For spin 1 vector field, there is only a massless zero mode on the bent brane. For spin 1/2 fermion field, it is shown that, in the case of no Yukawa coupling of scalar-fermion, there is no existence of localized massless zero mode for both left and right chiral fermions. In order to localize massless fermions, some kind of Yukawa coupling must be included. We study two types of Yukawa couplings as examples. Localization property of chiral fermions is related to the parameters of the brane model, the Yukawa coupling constant and the cosmological constant of the 4-dimensional space–time.     

Dynamics of Multiple Scalar Fields Model of Dark Energy with Spatial Curvature

The dynamical system of multiple scalar fields in FRW universe with different spatial curvature have been analyzed in this paper. In the radiation-dominated phase, the constant curvature factor k does not work on the cosmic dynamical behaviors, including the scaling solution, energy density parameter and equation-of-state parameter. These aspects are affected by curvature factor k in the matter-dominated phase. In the special scalar field-dominated phase, the energy density parameter normalization restricts the Universe is spatial flat and the curvature factor k is not present in the dynamics. In this paper, the Universe is closed in the matter-dominated phase, and flat in the scalar field-dominated phase. The spatial flatness and the w _ϕ =−1 in the third phase are coincide with the current observations.     

Scalar field dynamics on a brane

The dynamics of a flat isotropic brane Universe with two-component matter source —perfect fluid with the equation of statep = (γ − 1)ρ and a scalar field with a power-law potentialV ∼ φ^α is investigated. We describe solutions for which the scalar field energy density scales as a power-law of the scale factor. We also describe solutions existing in regions of the parameter space where these scaling solutions are unstable or do not exist.     

Axiomatic renormalization of the stress tensor of a conformally invariant field in conformally flat spacetimes

Using only the general properties which the renormalized stress-energy tensor T_μν should satisfy—and not relying on any assumptions associated with specific renormalization techniques—we derive the expression for T_μν for conformally invariant fields in conformally flat spacetimes of two and four dimensions. In two dimensions, these arguments rederive the Davies-Fulling-Unruh expression for the stress tensor of a scalar field; in four dimensions the results agree with those of Brown and Cassidy, except that we exclude the local curvature term depending on fourth-order derivatives of the metric. The dynamics of a k = 0 Robertson-Walker universe filled with radiation of the conformally invariant field is investigated and it is found that the equations cease to admit a solution when the Planck density is reached.