We investigate the presence of defects in systems described by real scalar field in (D,1) spacetime dimensions. We show that when the potential assumes specific form, there are models which support stable global defects for D arbitrary. We also show how to find first-order differential equations that solve the equations of motion, and how to solve models in D dimensions via soluble problems in D=1. We illustrate the procedure examining specific models and finding explicit solutions.PACS numbers: 11.10. Lm, 11.27.+d, 98.80.Cq The search for defect structures of topological nature is of direct interest to high energy physics, in particular to gravity in warped spacetimes involving D spatial extra dimensions. Very recently, a great deal of attention has been given to scalar fields coupled to gravity in (4, 1) dimensions [1,2,3,4,5]. Our interest here is related to Ref. [6], which deals with critical behavior of thick branes induced at high temperature, and to Refs. [7,8,9], which study the coupling of scalar and other fields to gravity in warped spacetimes involving two or more extra dimensions.These specific investigations have motivated us to study defect solutions in models involving scalar field in (D, 1) spacetime dimensions. To do this, however, we have to circumvent a theorem [10,11,12], which states that models described by a single real scalar field cannot support topological defects, unless we work in (1, 1) space-time dimensions. To evade this problem, in the present letter we consider models described by the La-, and φ is a real scalar field. The metric is (+, −, . . . , −), withis a smooth function of φ, and W φ = dW/dφ. We suppose thatφ is a critical point of V , such that V (φ) = 0. This generalization is different from the extensions one usually considers to evade the aforementined problem, which include for instance constraints in the scalar fields and/or the presence of fields with nonzero spin -see, e.g., Ref. [13], and other specific works on the subject [14,15]. Potentials of the above form appear for instance in the Gross-Pitaevski equation, which finds applications in several branches of physics -see, e.g., Ref. [16]. Other recent examples in (1, 1) dimensions include Ref. [17], which deals with the dynamics of embedded kinks, and Refs. [18], which describe scalar field in distinct backgrounds.In higher dimensions, the factor 1/r N that we introduce in Eq. (1) gives rise to an effective model, which comes from a more fundamental theory. To make this point clear, we consider the modelµν , which is a simplified Abelian version of the color dielectric model [19] in the absence of fermionssee, e.g., Ref. [20]. This model describes coupling between the real scalar field and the gauge field A µ , through the dielectric function f (φ). Here F µν = ∂ µ A ν − ∂ ν A µ is the gauge field strenght. This model shows that for spherically symmetric static configurations in the electric sector, the equation of motion for the matter field is ∇φ + (df /dφ)E 2 r = 0, where E = (E r , 0, ..., 0) is the electr...

We investigate the presence of defect structures in generalized models described by real scalar field in (1, 1) space-time dimensions. We work with two distinct generalizations, one in the form of a product of functions of the field and its derivative, and the other as a sum. We search for static solutions and study the corresponding linear stability on general grounds. We illustrate the results with several examples, where we find stable defect structures of modified profile. In particular, we show how the new defect solutions may give rise to evolutions not present in the standard scenario in higher spatial dimensions.

We study the evolution of maximally symmetric p-branes with a Sp−i ⊗ Ê i topology in flat expanding or collapsing homogeneous and isotropic universes with N + 1 dimensions (with N ≥ 3, p < N , 0 ≤ i < p). We find the corresponding equations of motion and compute new analytical solutions for the trajectories in phase space. For a constant Hubble parameter, H, and i = 0 we show that all initially static solutions with a physical radius below a certain critical value, r 0 c , are periodic while those with a larger initial radius become frozen in comoving coordinates at late times. We find a stationary solution with constant velocity and physical radius, rc, and compute the root mean square velocity of the periodic p-brane solutions and the corresponding (average) equation of state of the p-brane gas. We also investigate the p-brane dynamics for H = constant in models where the evolution of the universe is driven by a perfect fluid with constant equation of state parameter, w = Pp/ρp, and show that a critical radius, rc, can still be defined for −1 ≤ w < wc with wc = (2 − N )/N . We further show that for w ∼ wc the critical radius is given approximately by rcH ∝ (wc − w) γc with γc = −1/2 (rcH → ∞ when w → wc). Finally, we discuss the impact that the large scale dynamics of the universe can have on the macroscopic evolution of very small loops.

This work deals with braneworld models driven by real scalar fields with nonstandard dynamics. We develop the first-order formalism for models with standard gravity but with the scalar fields having generalized dynamics. We illustrate the results with examples of current interest, and we find analytical and numerical solutions for warp factors and scalar fields. The results indicate that the generalized braneworld scenario is classically stable, and capable of localizing gravity.