Recent developments in the physics of extra dimensions have opened up new avenues to test such theories. We review cosmological aspects of brane world scenarios such as the Randall–Sundrum brane model and two-brane systems with a bulk scalar field. We start with the simplest brane world scenario leading to a consistent cosmology: a brane embedded in an anti-de Sitter space–time. We generalize this setting to the case with a bulk scalar field and then to two-brane systems.We discuss different ways of obtaining a low-energy effective theory for two-brane systems, such as the moduli space approximation and the low-energy expansion. A comparison between the different methods is given. Cosmological perturbations are briefly discussed as well as early universe scenarios such as the cyclic model and the born-again brane world model. Finally we also present some physical consequences of brane world scenarios on the cosmic microwave background and the variation of constants.

Brane world cosmology

This paper gives a comprehensive review on thick brane solutions and related topics. Such models have attracted much attention from many aspects since the birth of the brane world scenario. In many works, it has been usually assumed that a brane is an infinitely thin object; however, in more general situations, one can no longer assume this. It is also widely considered that more fundamental theories such as string theory would have a minimal length scale. Many multidimensional field theories coupled to gravitation have exact solutions of gravitating topological defects, which can represent our brane world. The inclusion of brane thickness can realize a variety of possible brane world models. Given our understanding, the known solutions can be classified into topologically non-trivial solutions and trivial ones. The former class contains solutions of a single scalar (domain walls), multi-scalar, gauge-Higgs (vortices), Weyl gravity and so on. As an example of the latter class, we consider solutions of two interacting scalar fields. Approaches to obtain cosmological equations in the thick brane world are reviewed. Solutions with spatially extended branes (S-branes) and those with an extra time-like direction are also discussed.

Thick brane solutions

The Gauss-Codazzi formalism is used to obtain exact solutions to Einstein's equations in the presence of domain walls. Domain walls are shown to have repulsive gravitational fields. The most general solution to Einstein's equations for a planar domain wall is obtained. Also, the motion of a spherical domain wall in an asymptotically flat space-time is derived.

The Gravitationally Repulsive Domain Wall

We present the white dwarf sequence of the globular cluster M4, based on a 123 orbit Hubble Space Telescope exposure, with a limiting magnitude of V ~ 30 and I ~ 28. The white dwarf luminosity function rises sharply for I > 25.5, consistent with the behavior expected for a burst population. The white dwarfs of M4 extend to approximately 2.5 mag fainter than the peak of the local Galactic disk white dwarf luminosity function. This demonstrates a clear and significant age difference between the Galactic disk and the halo globular cluster M4. Using the same standard white dwarf models to fit each luminosity function yields ages of 7.3 ± 1.5 Gyr for the disk and 12.7 ± 0.7 Gyr for M4 (2 σ statistical errors).

The White Dwarf cooling sequence in the Globular Cluster Messier 4

We analyze the cosmological signatures visible to an observer in a Coleman-de Luccia bubble when another such bubble collides with it. We use a gluing procedure to generalize the results of Freivogel, Horowitz and Shenker to the case of a general cosmological constant in each bubble and study the resulting spacetimes. The collision breaks the isotropy and homogeneity of the bubble universe and provides a cosmological 'axis of evil' which can affect the cosmic microwave background in several unique and potentially detectable ways. Unlike more conventional perturbations to the inflationary initial state, these signatures can survive even relatively long periods of inflation. In addition, we find that for a given collision the observers in the bubble with smaller cosmological constant are safest from collisions with domain walls, possibly providing another anthropic selection principle for small positive vacuum energy.

When Worlds Collide

It is intriguing to consider the possibility that the big bang of the standard (3+1)-dimensional cosmology originated from the collision of two branes within a higher dimensional spacetime, leading to the production of a large amount of entropy. In this paper we study, subject to certain well-defined assumptions, under what conditions such a collision leads to an expanding universe. We assume the absence of novel physics, so that ordinary (4+1)-dimensional Einstein gravity remains a valid approximation. It is necessary that the fifth dimension not become degenerate at the moment of collision. First the case of a symmetric collision of infinitely thin branes having a hyperbolic or flat spatial geometry is considered. We find that a symmetric collision results in a collapsing universe on the final brane unless the preexisting expansion rate in the bulk just prior to the collision is sufficiently large in comparison to the momentum transfer in the fifth dimension. Such prior expansion may either result from negative spatial curvature or from a positive five-dimensional cosmological constant. The relevance of these findings to the colliding bubble braneworld universe scenario is discussed. Finally, results from a numerical study of colliding thick-wall branes is presented, which confirm the results of the thin-wall approximation.

When do colliding bubbles produce an expanding universe

Concepts developed in the gravitational lensing techniques such as shear, convergence, tangential, and radial arcs maybe used to see how tenable inhomogeneous models proposed to explain the acceleration of the universe models are. We study the widely discussed Lemaitre-Tolman-Bondi (LTB) cosmological models. It turns out that for the observer sitting at origin of a global LTB solution the shear vanishes as in the Friedmann-Robertson-Walker models, while the value of convergence is different, which may lead to observable cosmological effects. We also consider Swiss-cheese models proposed recently based on LTB with an observer sitting in the Friedmann-Robertson-Walker part. It turns out that they have different behavior as far as the formation of radial and tangential arcs are concerned.

Lensing effects in inhomogeneous cosmological models

There exist many observational evidences implying the expansion of our Universe is undergoing a late-time acceleration; the mechanism of this acceleration is yet unknown. In the so-called thick brane model this phenomena is attributed to the thickness of the brane along the extra dimension. In this study we mainly rely on the consistency of this model with most recent observational data related to the background evolution. The new Supernova Type Ia (SNIa) Gold sample and Supernova Legacy Survey (SNLS) data, the position of the acoustic peak at the last scattering surface from the Wilkinson Microwave Anisotropy Probe (WMAP) observations and the baryon acoustic oscillation peak found in the Sloan Digital Sky Survey (SDSS) are used to constrain the free parameter of the thick codimension 1 brane model. To infer its consistency with the age of our Universe, we compare the age of old cosmological objects with what computed using the best-fit values for the model parameters. When the Universe is matter dominated, $w=0$, at 68% level of confidence, the combination of the Gold sample SNIa, cosmic microwave background (CMB) shift parameter and SDSS databases provide ${\ensuremath{\Omega}}_{m}={0.31}_{\ensuremath{-}0.02}^{+0.02}$, ${\ensuremath{\Omega}}_{\mathcal{C}}={0.05}_{\ensuremath{-}0.01}^{+0.01}$, ${w}_{r}=\ensuremath{-}{1.40}_{\ensuremath{-}0.20}^{+0.20}$, hence a spatially open universe with ${\ensuremath{\Omega}}_{k}={0.21}_{\ensuremath{-}0.08}^{+0.08}$. The same combination with the SNLS supernova observation gives ${\ensuremath{\Omega}}_{m}={0.28}_{\ensuremath{-}0.02}^{+0.03}$, ${\ensuremath{\Omega}}_{\mathcal{C}}={0.037}_{\ensuremath{-}0.004}^{+0.003}$, ${w}_{r}=\ensuremath{-}{2.05}_{\ensuremath{-}0.15}^{+0.15}$ consequently provides a spatially open universe ${\ensuremath{\Omega}}_{k}={0.11}_{\ensuremath{-}0.07}^{+0.10}$. These results obviously seem to be in contradiction with the most recent WMAP results indicating a flat universe.

Is the thick brane model consistent with recent observations

We present the generalized Friedmann equations describing the cosmological evolution of a finite thick brane immeresed in a five-dimensional Schwarzschild Anti-de Sitter spacetime. A linear term in the density in addition to a quatratic one arises in the Friedmann equation, leading to the standard cosmological evolution at late times without introducing an ad hoc tension term for the brane. The effective four-dimensional cosmological constant is then uplifted similar to the KKLT effect and vanishes for a brane thickness equal to the AdS curvature size, up to the third order of the thickness. The four-dimensional gravitational constant is then equal to the five-dimensional one divided by the AdS curvature radius, similar to that derived by dimensional compactification. An accelerating brane cosmology may emerge at late times provided there is either a negative transverse pressure component in the brane energy-momentum tensor or the effective brane cosmological constant is positive.

Generalized Friedmann equations for a finite thick brane

We consider a planar gravitating thick domain wall of the λϕ4 theory as a space–time with finite thickness glued to two vacuum space–times on each side of it. Darmois junction conditions written on the boundaries of the thick wall with the embedding space–times reproduce the Israel junction condition across the wall in the limit of infinitesimal thickness. The thick planar domain wall located at a fixed position is then transformed to a new coordinate system in which its dynamics can be formulated. It is shown that the wall's core expands as if it were a thin wall. The thickness in the new coordinates is not constant anymore and its time dependence is given.

Sima Ghassemi

Papers

When do colliding bubbles produce an expanding universe

Lensing effects in inhomogeneous cosmological models

Is the thick brane model consistent with recent observations

Generalized Friedmann equations for a finite thick brane

Thick planar domain wall: its thin wall limit and dynamics