A class of generalized Randall-Sundrum type II (RS) brane-world models with Weyl fluid are confronted with the Gold supernovae data set and BBN constraints. We consider three models with different evolutionary history of the Weyl fluid, characterized by the parameter $α$. For $α=0$ the Weyl curvature of the bulk appears as dark radiation on the brane, while for $α=2$ and 3 the brane radiates, leaving a Weyl fluid on the brane with energy density decreasing slower than that of (dark) matter. In each case the contribution $Ω_d$ of the Weyl fluid represents but a few percent of the energy content of the Universe. All models fit reasonably well the Gold2006 data. The best fit model for $α=0$ is for $Ω_d=0.04$. In order to obey BBN constraints in this model however, the brane had to radiate at earlier times.
We develop a technique to study relativistic perturbations in the generalised brane cosmological scenario, which is a generalisation of the multi-fluid cosmological perturbations to brane cosmology. The novelty of the technique lies in the inclusion of a radiative bulk which is responsible for bulk-brane energy exchange, and in turn, modifies the standard perturbative analysis to a great extent. The analysis involves a geometric fluid -- called the Weyl fluid -- whose nature and role have been studied extensively both for the empty bulk and the radiative bulk scenario. Subsequently, we find th…
We study the behavior of spatially homogeneous brane-worlds close to the initial singularity in the presence of both local and nonlocal stresses. It is found that the singularity in these brane-worlds can be locally either isotropic or anisotropic. We then investigate the Weyl curvature conjecture, according to which some measure of the Weyl curvature is related to a gravitational entropy. In particular, we study the Weyl curvature conjecture on the brane with respect to the dimensionless ratio of the Weyl invariant and the Ricci square and the measure proposed by Grøn and Hervik. We also argu…
In brane-world cosmologies of Randall-Sundrum type, we show that evolution of large-scale curvature perturbations may be determined on the brane, without solving the bulk perturbation equations. The influence of the bulk gravitational field on the brane is felt through a projected Weyl tensor which behaves effectively like an imperfect radiation fluid with anisotropic stress. We define curvature perturbations on uniform density surfaces for both the matter and Weyl fluids, and show that their evolution on large scales follows directly from the energy conservation equations for each fluid. The …
We show how braneworld cosmology with bulk matter can explain structure formation. In this scenario, the nonlocal corrections to the Friedmann equations supply a Weyl fluid that can dominate over matter at late times due to the energy exchange between the brane and the bulk. We demonstrate that the presence of the Weyl fluid radically changes the perturbation equations, which can take care of the fluctuations required to account for the large amount of inhomogeneities observed in the local universe. Further, we show how this Weyl fluid can mimic dark matter. We also investigate the bulk geomet…
In the context of the Randall-Sundrum (RS) single-brane scenario, we discuss the bulk geometry and dynamics of a cosmological brane in terms of the local energy conservation law which exists for the bulk that allows slicing with a maximally symmetric 3-space. This conservation law enables us to define a local mass in the bulk. We show that there is a unique generalization of the dark radiation on the brane, which is given by the local mass. We find there also exists a conserved current associated with the Weyl tensor, and the corresponding local charge, which we call the Weyl charge, is given …
In this paper we deal with the cosmological dynamics of Randall-Sundrum brane-world type scenarios in which the five-dimensional Weyl tensor has a non-vanishing projection onto the three-brane where matter fields are confined. Using dynamical systems techniques, we study how the state space of Friedmann-Lemaitre-Robertson-Walker (FLRW) and Bianchi type I cosmological models is affected by the bulk Weyl tensor, focusing in the differences that appear with respect to general relativity and also Randall-Sundrum cosmological scenarios without the Weyl tensor contribution.
We first obtain the analogue of Vaidya's solution on the brane for studying the collapse of null fluid onto a flat Minkowski cavity on the brane. Since the back-reaction of the bulk onto the brane is supposed to strengthen gravity on the brane, it would favour formation of black hole as against naked singularity. That is the parameter window in the initial data set giving rise to naked singularity in the 4D Vaidya case would now get partially covered.
The luminosity distance - redshift relation for a wide class of generalized Randall-Sundrum type II brane-world models with Weyl fluid is compared to the presently available supernova data. We find that there is a class of spacially flat models with different amounts of matter $Ω_ρ$ and Weyl fluid $Ω_{d}$, which have a very similar fitting quality. The best-fit models are equally likely and can be regarded as extensions of the $Λ$CDM model, which is also included. We examine three models with different evolutionary history of the Weyl fluid, characterized by a parameter $α=0,~2$ and$~3$. The f…
It is shown that (except for two well defined cases), the necessary and sufficient condition for any spherically symmetric distribution of fluid to leave the state of equilibrium (or quasi-equilibrium), is that the Weyl tensor changes with respect to its value in the state of equilibrium (or quasi-equilibrium).
We propose a new formulation to calculate the Cosmic Microwave Background (CMB) spectrum in the Randall Sundrum two-branes model based on recent progresses in solving the bulk geometry using a low energy approximation. The evolution of the anisotropic stress imprinted on the brane by the 5D Weyl tensor is calculated. An impact of the dark radiation perturbation on CMB spectrum is investigated in a simple model assuming an initially scale-invariant adiabatic perturbations. The dark radiation perturbation induces isocurvature perturbations, but the resultant spectrum can be quite different from …
We study in a self-consistent way the impact of the emission of bulk gravitons on the (homogeneous) cosmology of a three-brane embedded in a five-dimensional spacetime. In the low energy regime, we recover the well known result that the bulk affects the Friedmann equation only via a radiation-like term $\C/a^4$, called dark or Weyl radiation. By contrast, in the high energy regime, we find that the Weyl parameter $\C$ is no longer constant but instead grows very rapidly as $\C\propto a^4$. As a consequence, the value of $\C$ today is not a free parameter as usually considered but is a fixed nu…
We study cosmological perturbations in a brane-world scenario where the matter fields live on a four-dimensional brane and gravity propagates in the five-dimensional bulk. We present the equations of motion in an arbitrary gauge for metric perturbations in the bulk and matter perturbations on the brane. Gauge-invariant perturbations are then constructed corresponding to perturbations in longitudinal and Gaussian normal gauges. Longitudinal gauge metric perturbations may be directly derived from three master variables (separately describing scalar, vector and tensor metric perturbations) which …
Recent developments in string theory have led to 5-dimensional warped spacetime models in which standard-model fields are confined to a 3-brane (the observed universe), while gravity can propagate in the fifth dimension. Gravity is localized near the brane at low energies, even if the extra dimension is noncompact. A review is given of the classical geometry and dynamics of these brane-world models. The field equations on the brane modify the general relativity equations in two ways: local 5-D effects are imprinted on the brane as a result of its embedding, and are significant at high energies…
An analysis of a spherically symmetric braneworld configuration is performed when the intrinsic curvature scalar is included in the bulk action. In the case when the electric part of the Weyl tensor is zero, all the exterior solutions are found; one of them is of the Schwarzschild-(A)dS(4) form, which is matched to a modified Oppenheimer-Volkoff interior solution. In the case when the electric part of the Weyl tensor is non zero, the exterior Schwarzschild-(A)dS(4) black hole solution is modified receiving corrections from the non-local bulk effects. A non-universal gravitational constant aris…
We introduce brane-worlds with non-constant tension, strenghtening the analogy with fluid membranes, which exhibit a temperature-dependence according to the empirical law established by Eötvös. This new degree of freedom allows for evolving gravitational and cosmological constants, the latter being a natural candidate for dark energy. We establish the covariant dynamics on a brane with variable tension in full generality, by considering asymmetrically embedded branes and allowing for non-standard model fields in the 5-dimensional space-time. Then we apply the formalism for a perfect fluid on a…
We carefully investigate the gravitational perturbation of the Randall-Sundrum (RS) single brane-world solution [hep-th/9906064], based on a covariant curvature tensor formalism recently developed by us. Using this curvature formalism, it is known that the `electric' part of the 5-dimensional Weyl tensor, denoted by $E_{μν}$, gives the leading order correction to the conventional Einstein equations on the brane. We consider the general solution of the perturbation equations for the 5-dimensional Weyl tensor caused by the matter fluctuations on the brane. By analyzing its asymptotic behaviour i…
We investigate whether dark matter can be replaced by various source terms appearing in the effective Einstein equation, valid on a brane embedded into a higher dimensional space-time (the bulk). Such non-conventional source terms include a quadratic (ordinary) matter source term, a geometric source term originating in the Weyl curvature of the bulk, a source term arising from the possible asymmetric embedding, and finally the pull-back to the brane of possible non-standard model bulk fields.
We study charged brane-world black holes in the model of Randall and Sundrum in which our universe is viewed as a domain wall in asymptotically anti-de Sitter space. Such black holes can carry two types of ``charge'', one arising from the bulk Weyl tensor and one from a gauge field trapped on the wall. We use a combination of analytical and numerical techniques to study how these black holes behave in the bulk. It has been shown that a Reissner-Nordstrom geometry is induced on the wall when only Weyl charge is present. However, we show that such solutions exhibit pathological features in the b…
The Friedmann law on the brane generically depends quadratically on the brane energy density and involves a ``dark radiation'' term due to the bulk Weyl tensor. Despite its unfamiliar form, we show how it can be derived from a standard four-dimensional Brans-Dicke theory at low energy. In particular, the dark radiation term is found to depend linearly on the brane energy densities. For any equation of state on the branes, the radion evolves such as to generate radiation-dominated cosmology. The radiation-dominated era is conventional and consistent with nucleosynthesis.
In Randall-Sundrum-type brane-world cosmologies, density perturbations generate Weyl curvature in the bulk, which in turn backreacts on the brane via stress-energy perturbations. On large scales, the perturbation equations contain a closed system on the brane, which may be solved without solving for the bulk perturbations. Bulk effects produce a non-adiabatic mode, even when the matter perturbations are adiabatic, and alter the background dynamics. As a consequence, the standard evolution of large-scale fluctuations in general relativity is modified. The metric perturbation on large-scales is …
