Localizing gravity on thick branes: a solution for massive KK modes of the Schroedinger equation

We generate scalar thick brane configurations in a 5D Riemannian space time which describes gravity coupled to a self-interacting scalar field. We also show that 4D gravity can be localized on a thick brane which does not necessarily respect Z_2-symmetry, generalizing several previous models based on the Randall-Sundrum system and avoiding the restriction to orbifold geometries as well as the introduction of the branes in the action by hand. We begin by obtaining a smooth brane configuration that preserves 4D Poincar'e invariance and violates reflection symmetry along the fifth dimension. The extra dimension can have either compact or extended topology, depending on the values of the parameters of the solution. In the non-compact case, our field configuration represents a thick brane with positive energy density centered at y=c_2, whereas in the compact case we get pairs of thick branes. We recast as well the wave equations of the transverse traceless modes of the linear fluctuations of the classical solution into a Schroedinger's equation form with a volcano potential of finite bottom. We solve Schroedinger equation for the massless zero mode m^2=0 and obtain a single bound wave function which represents a stable 4D graviton and is free of tachyonic modes with m^2<0. We also get a continuum spectrum of Kaluza-Klein (KK) states with m^2>0 that are suppressed at y=c_2 and turn asymptotically into plane waves. We found a particular case in which the Schroedinger equation can be solved for all m^2>0, giving us the opportunity of studying analytically the massive modes of the spectrum of KK excitations, a rare fact when considering thick brane configurations.Comment: 8 pages in latex. We corrected signs in the field equations, the expressions for the scalar field and the self-interacting potential. Due to the fact that no changes are introduced in the warp factor, the physics of the system remains the sam

The phase portrait of a matter bounce in Horava-Lifshitz cosmology

The occurrence of a bounce in FRW cosmology requires modifications of general relativity. An example of such a modification is the recently proposed Horava-Lifshitz theory of gravity, which includes a ``dark radiation'' term with a negative coefficient in the analog of the Friedmann equation. This paper describes a phase space analysis of models of this sort with the aim of determining to what extent bouncing solutions can occur. A simplification, valid in the relevant region, allows a reduction of the dimension of phase space so that visualization in three dimensions is possible. It is found that a bounce is possible, but not generic in models under consideration. Apart from previously known bouncing solutions some new ones are also described. Other interesting solutions found include ones which describe a novel sort of oscillating universes.Comment: 14 pages, 8 figure

Pathological behaviour of the scalar graviton in Ho\v{r}ava-Lifshitz gravity

We confirm the recent claims that, in the infrared limit of Ho\v{r}ava-Lifshitz gravity, the scalar graviton becomes a ghost if the sound speed squared is positive on the flat de Sitter and Minkowski background. In order to avoid the ghost and tame the instability, the sound speed squared should be negative and very small, which means that the flow parameter $\lambda$ should be very close to its General Relativity (GR) value. We calculate the cubic interactions for the scalar graviton which are shown to have a similar structure with those of the curvature perturbation in k-inflation models. The higher order interactions become increasing important for a smaller sound speed squared, that is, when the theory approaches GR. This invalidates any linearized analysis and any predictability is lost in this limit as quantum corrections are not controllable. This pathological behaviour of the scalar graviton casts doubt on the validity of the projectable version of the theory.Comment: 7 pages, references added; v3: Typos corrected, minor changes to text and precise determination of the strong coupling scale. Replaced to match published version

Braneworld models with a non-minimally coupled phantom bulk field: a simple way to obtain the -1-crossing at late times

We investigate general braneworld models, with a non-minimally coupled phantom bulk field and arbitrary brane and bulk matter contents. We show that the effective dark energy of the brane-universe acquires a dynamical nature, as a result of the non-minimal coupling which provides a mechanism for an indirect "bulk-brane interaction" through gravity. For late-time cosmological evolution and without resorting to special ansatzes or to specific areas of the parameter space, we show that the -1-crossing of its equation-of-state parameter is general and can be easily achieved. As an example we provide a simple, but sufficiently general, approximate analytical solution, that presents the crossing behavior.Comment: 11 pages, 2 figure

Remarks on the Scalar Graviton Decoupling and Consistency of Horava Gravity

Recently Horava proposed a renormalizable gravity theory with higher derivatives by abandoning the Lorenz invariance in UV. But there have been confusions regarding the extra scalar graviton mode and the consistency of the Horava model. I reconsider these problems and show that, in the Minkowski vacuum background, the scalar graviton mode can be consistency decoupled from the usual tensor graviton modes by imposing the (local) Hamiltonian as well as the momentum constraints.Comment: Some clarifications regarding the projectable case added, Typos corrected, Comments (Footnote No.9, Note Added) added, References updated, Accepted in CQ

Detailed balance condition and ultraviolet stability of scalar field in Horava-Lifshitz gravity

Detailed balance and projectability conditions are two main assumptions when Horava recently formulated his theory of quantum gravity - the Horava-Lifshitz (HL) theory. While the latter represents an important ingredient, the former often believed needs to be abandoned, in order to obtain an ultraviolet stable scalar field, among other things. In this paper, because of several attractive features of this condition, we revisit it, and show that the scalar field can be stabilized, if the detailed balance condition is allowed to be softly broken. Although this is done explicitly in the non-relativistic general covariant setup of Horava-Melby-Thompson with an arbitrary coupling constant $\lambda$, generalized lately by da Silva, it is also true in other versions of the HL theory. With the detailed balance condition softly breaking, the number of independent coupling constants can be still significantly reduced. It is remarkable to note that, unlike other setups, in this da Silva generalization, there exists a master equation for the linear perturbations of the scalar field in the flat Friedmann-Robertson-Walker background.Comment: Some typos are corrected. To appear in JCA

DGP Cosmology with a Non-Minimally Coupled Scalar Field on the Brane

We construct a DGP inspired braneworld scenario where a scalar field non-minimally coupled to the induced Ricci curvature is present on the brane. First we investigate the status of gravitational potential with non-minimal coupling and observational constraints on this non-minimal model. Then we further deepen the idea of embedding of FRW cosmology in this non-minimal setup. Cosmological implications of this scenario are examined with details and the quintessence and late-time expansion of the universe within this framework are examined. Some observational constraints imposed on this non-minimal scenario are studied and relation of this model with dark radiation formalism is determined with details.Comment: 26 pages, 3 eps figure

Localization of gravity on a de Sitter thick braneworld without scalar fields

In this work we present a simple thick braneworld model that is generated by an intriguing interplay between a 5D cosmological constant with a de Sitter metric induced in the 3-brane without the inclusion of scalar fields. We show that 4D gravity is localized on this brane, provide analytic expressions for the massive Kaluza-Klein (KK) fluctuation modes and also show that the spectrum of metric excitations displays a mass gap. We finally present the corrections to Newton's law due to these massive modes. This model has no naked singularities along the fifth dimension despite the existence of a mass gap in the graviton spectrum as it happens in thick branes with 4D Poincare symmetry, providing a simple model with very good features: the curvature is completely smooth along the fifth dimension, it localizes 4D gravity and the spectrum of gravity fluctuations presents a mass gap, a fact that rules out the existence of phenomenologically dangerous ultralight KK excitations in the model. We finally present our solution as a limit of scalar thick branes.Comment: 11 pages in latex, no figures, title and abstract changed, a new section and some references adde

The Cosmological Constant and Horava-Lifshitz Gravity

Horava-Lifshitz theory of gravity with detailed balance is plagued by the presence of a negative bare (or geometrical) cosmological constant which makes its cosmology clash with observations. We argue that adding the effects of the large vacuum energy of quantum matter fields, this bare cosmological constant can be approximately compensated to account for the small observed (total) cosmological constant. Even though we cannot address the fine-tuning problem in this way, we are able to establish a relation between the smallness of observed cosmological constant and the length scale at which dimension 4 corrections to the Einstein gravity become significant for cosmology. This scale turns out to be approximately 5 times the Planck length for an (almost) vanishing observed cosmological constant and we therefore argue that its smallness guarantees that Lorentz invariance is broken only at very small scales. We are also able to provide a first rough estimation for the infrared values of the parameters of the theory $\mu$ and $Lambda_w$.Comment: 9 pages, Late

Mass hierarchy, mass gap and corrections to Newton's law on thick branes with Poincare symmetry

We consider a scalar thick brane configuration arising in a 5D theory of gravity coupled to a self-interacting scalar field in a Riemannian manifold. We start from known classical solutions of the corresponding field equations and elaborate on the physics of the transverse traceless modes of linear fluctuations of the classical background, which obey a Schroedinger-like equation. We further consider two special cases in which this equation can be solved analytically for any massive mode with m^2>0, in contrast with numerical approaches, allowing us to study in closed form the massive spectrum of Kaluza-Klein (KK) excitations and to compute the corrections to Newton's law in the thin brane limit. In the first case we consider a solution with a mass gap in the spectrum of KK fluctuations with two bound states - the massless 4D graviton free of tachyonic instabilities and a massive KK excitation - as well as a tower of continuous massive KK modes which obey a Legendre equation. The mass gap is defined by the inverse of the brane thickness, allowing us to get rid of the potentially dangerous multiplicity of arbitrarily light KK modes. It is shown that due to this lucky circumstance, the solution of the mass hierarchy problem is much simpler and transparent than in the (thin) Randall-Sundrum (RS) two-brane configuration. In the second case we present a smooth version of the RS model with a single massless bound state, which accounts for the 4D graviton, and a sector of continuous fluctuation modes with no mass gap, which obey a confluent Heun equation in the Ince limit. (The latter seems to have physical applications for the first time within braneworld models). For this solution the mass hierarchy problem is solved as in the Lykken-Randall model and the model is completely free of naked singularities.Comment: 25 pages in latex, no figures, content changed, corrections to Newton's law included for smooth version of RS model and an author adde