Bulk gravitons from a cosmological brane

We investigate the emission of gravitons by a cosmological brane into an Anti de Sitter five-dimensional bulk spacetime. We focus on the distribution of gravitons in the bulk and the associated production of `dark radiation' in this process. In order to evaluate precisely the amount of dark radiation in the late low-energy regime, corresponding to standard cosmology, we study numerically the emission, propagation and bouncing off the brane of bulk gravitons.Comment: 27 pages, 5 figures, minor corrections. Final versio

Moduli-Space Approximation for BPS Brane-Worlds

We develop the moduli-space approximation for the low energy regime of BPS-branes with a bulk scalar field to obtain an effective four-dimensional action describing the system. An arbitrary BPS potential is used and account is taken of the presence of matter in the branes and small supersymmetry breaking terms. The resulting effective theory is a bi-scalar tensor theory of gravity. In this theory, the scalar degrees of freedom can be stabilized naturally without the introduction of additional mechanisms other than the appropriate BPS potential. We place observational constraints on the shape of the potential and the global configuration of branes.Comment: 10 pages, 1 figur

(1+3) Covariant Dynamics of Scalar Perturbations in Braneworlds

We discuss the dynamics of linear, scalar perturbations in an almost Friedmann-Robertson-Walker braneworld cosmology of Randall-Sundrum type II using the 1+3 covariant approach. We derive a complete set of frame-independent equations for the total matter variables, and a partial set of equations for the non-local variables which arise from the projection of the Weyl tensor in the bulk. The latter equations are incomplete since there is no propagation equation for the non-local anisotropic stress. We supplement the equations for the total matter variables with equations for the independent constituents in a cold dark matter cosmology, and provide solutions in the high and low-energy radiation-dominated phase under the assumption that the non-local anisotropic stress vanishes. These solutions reveal the existence of new modes arising from the two additional non-local degrees of freedom. Our solutions should prove useful in setting up initial conditions for numerical codes aimed at exploring the effect of braneworld corrections on the cosmic microwave background (CMB) power spectrum. As a first step in this direction, we derive the covariant form of the line of sight solution for the CMB temperature anisotropies in braneworld cosmologies, and discuss possible mechanisms by which braneworld effects may remain in the low-energy universe.Comment: 22 pages replaced with additional references and minor corrections in Revtex4, and accepted for publication in Phys. Rev.

Bulk Gravitational Field and Cosmological Perturbations on the Brane

We investigate the effect of the bulk gravitational field on the cosmological perturbations on a brane embedded in the 5D Anti-de Sitter (AdS) spacetime. The effective 4D Einstein equations for the scalar cosmological perturbations on the brane are obtained by solving the perturbations in the bulk. Then the behaviour of the corrections induced by the bulk gravitational field to the conventional 4D Einstein equation are determined. Two types of the corrections are found. First we investigate the corrections which become significant at scales below the AdS curvature scales and in the high energy universe with the energy density larger than the tension of the brane. The evolution equation for the perturbations on the brane is found and solved. Another type of the corrections is induced on the brane if we consider the bulk perturbations which do not contribute to the metric perturbations but do contribute to the matter perturbations. At low energies, they have imaginary mass m^2=-(2/3) \k^2 in the bulk where \k is the 3D comoving wave number of the perturbations. They diverge at the horizon of the AdS spacetime. The induced density perturbations behave as sound waves with sound velocity $1/\sqrt{3}$ in the low energy universe. At large scales, they are homogeneous perturbations that depend only on time and decay like radiation. They can be identified as the perturbations of the dark radiation. They produce isocurvature perturbations in the matter dominated era. Their effects can be observed as the shifts of the location and the height of the acoustic peak in the CMB spectrum.Comment: 35 pages, 1 figur

Godel brane

We consider the brane-world generalisation of the Godel universe and analyse its dynamical interaction with the bulk. The exact homogeneity of the standard Godel spacetime no longer holds, unless the bulk is also static. We show how the anisotropy of the Godel-type brane is dictated by that of the bulk and find that the converse is also true. This determines the precise evolution of the nonlocal anisotropic stresses, without any phenomenological assumptions, and leads to a self-consistent closed set of equations for the evolution of the Godel brane. We also examine the causality of the Godel brane and show that the presence of the bulk cannot prevent the appearance of closed timelike curves.Comment: Revised version, to match paper published in Phys. Rev.

Brane cosmology with a bulk scalar field

We consider ``cosmologically symmetric'' (i.e. solutions with homogeneity and isotropy along three spatial dimensions) five-dimensional spacetimes with a scalar field and a three-brane representing our universe. We write Einstein's equations in a conformal gauge, using light-cone coordinates. We obtain explicit solutions: a. assuming proportionality between the scalar field and the logarithm of the (bulk) scale factor; b. assuming separable solutions. We then discuss the cosmology in the brane nduced by these solutions.Comment: 24 pages, Latex, no figur

Low Energy Branes, Effective Theory and Cosmology

The low energy regime of cosmological BPS-brane configurations with a bulk scalar field is studied. We construct a systematic method to obtain five-dimensional solutions to the full system of equations governing the geometry and dynamics of the bulk. This is done for an arbitrary bulk scalar field potential and taking into account the presence of matter on the branes. The method, valid in the low energy regime, is a linear expansion of the system about the static vacuum solution. Additionally, we develop a four-dimensional effective theory describing the evolution of the system. At the lowest order in the expansion, the effective theory is a bi-scalar tensor theory of gravity. One of the main features of this theory is that the scalar fields can be stabilized naturally without the introduction of additional mechanisms, allowing satisfactory agreement between the model and current observational constraints. The special case of the Randall-Sundrum model is discussed.Comment: 19 pages, 4 figure

Scalar perturbations from brane-world inflation

We investigate the scalar metric perturbations about a de Sitter brane universe in a 5-dimensional anti de Sitter bulk. We compare the master-variable formalism, describing metric perturbations in a 5-dimensional longitudinal gauge, with results in a Gaussian normal gauge. For a vacuum brane (with constant brane tension) there is a continuum of normalizable Kaluza-Klein modes, with m>3H/2, which remain in the vacuum state. A light radion mode, with m=\sqrt{2}H, satisfies the boundary conditions for two branes but is not normalizable in the single-brane case. When matter is introduced (as a test field) on the brane, this mode, together with the zero-mode and an infinite ladder of discrete tachyonic modes, become normalizable. However, the boundary condition requires the self-consistent 4-dimensional evolution of scalar field perturbations on the brane and the dangerous growing modes are not excited. These normalizable discrete modes introduce corrections at first-order to the scalar field perturbations computed in a slow-roll expansion. On super-Hubble scales, the correction is smaller than slow-roll corrections to the de Sitter background. However on small scales the corrections can become significant.Comment: 15 page

Cosmology of a brane radiating gravitons into the extra dimension

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 number, which, generically, depends only on the number of relativistic degrees of freedom at the high/low energy transition. Our estimated amount of Weyl radiation satisfies the present nucleosynthesis bounds.Comment: 12 page

Quantum fluctuations in brane-world inflation without inflaton on the brane

A Randall-Sundrum type brane-cosmological model in which slow-roll inflation on the brane is driven solely by a bulk scalar field was recently proposed by Himemoto and Sasaki. We analyze their model in detail and calculate the quantum fluctuations of the bulk scalar field $\phi$ with $m^2=V''(\phi)$. We decompose the bulk scalar field into the infinite mass spectrum of 4-dimensional fields; the field with the smallest mass-square, called the zero-mode, and the Kaluza-Klein modes above it with a mass gap. We find the zero-mode dominance of the classical solution holds if $|m^2|\bar\ell^2\ll1$, where $\bar{\ell}$ is the curvature radius of the effectively anti-de Sitter bulk, but it is violated if $|m^2|\bar\ell^2\gg1$, though the violation is very small. Then we evaluate the vacuum expectation value $$ on the brane. We find the zero-mode contribution completely dominates if $|m^2|\bar{\ell}^2\ll 1$ similar to the case of classical background. In contrast, we find the Kaluza-Klein contribution is small but non-negligible if the value of $|m^2|\bar{\ell}^2$ is large.Comment: 12pages, 1 figure, typos corrected, a couple of paragraphs modified but no major change in the text, final version to be published in PR