Lemaitre-Tolman-Bondi model and accelerating expansion

I discuss the spherically symmetric but inhomogeneous Lemaitre-Tolman- Bondi (LTB) metric, which provides an exact toy model for an inhomogeneous universe. Since we observe light rays from the past light cone, not the expansion of the universe, spatial variation in matter density and Hubble rate can have the same effect on redshift as acceleration in a perfectly homogeneous universe. As a consequence, a simple spatial variation in the Hubble rate can account for the distant supernova data in a dust universe without any dark energy. I also review various attempts towards a semirealistic description of the universe based on the LTB model.Comment: Invited Review for a special Gen. Rel. Grav. issue on Dark Energy. 17 pages, 3 figure

Electromagnetic Casimir energy with extra dimensions

We calculate the energy-momentum tensor due to electromagnetic vacuum fluctuations between two parallel hyperplanes in more than four dimensions, considering both metallic and MIT boundary conditions. Using the axial gauge, the problem can be mapped upon the corresponding problem with a massless, scalar field satisfying respectively Dirichlet or Neumann boundary conditions. The pressure between the plates is constant while the energy density is found to diverge at the boundaries when there are extra dimensions. This can be related to the fact that Maxwell theory is then no longer conformally invariant. A similar behavior is known for the scalar field where a constant energy density consistent with the pressure can be obtained by improving the energy-momentum tensor with the Huggins term. This is not possible for the Maxwell field. However, the change in the energy-momentum tensor with distance between boundaries is finite in all cases.Comment: 16 pages, typos corrected, published versio

CMB anisotropies seen by an off-center observer in a spherically symmetric inhomogeneous universe

The current authors have previously shown that inhomogeneous, but spherically symmetric universe models containing only matter can yield a very good fit to the SNIa data and the position of the first CMB peak. In this work we examine how far away from the center of inhomogeneity the observer can be located in these models and still fit the data well. Furthermore, we investigate whether such an off-center location can explain the observed alignment of the lowest multipoles of the CMB map. We find that the observer has to be located within a radius of 15 Mpc from the center for the induced dipole to be less than that observed by the COBE satellite. But for such small displacements from the center, the induced quadru- and octopoles turn out to be insufficiently large to explain the alignment.Comment: 8 pages (REVTeX4), 7 figures; v2: minor changes, matches published versio

Quantum buoyancy, generalized second law, and higher-dimensional entropy bounds

Bekenstein has presented evidence for the existence of a universal upper bound of magnitude $2\pi R/\hbar c$ to the entropy-to-energy ratio $S/E$ of an arbitrary {\it three} dimensional system of proper radius $R$ and negligible self-gravity. In this paper we derive a generalized upper bound on the entropy-to-energy ratio of a $(D+1)$-dimensional system. We consider a box full of entropy lowered towards and then dropped into a $(D+1)$-dimensional black hole in equilibrium with thermal radiation. In the canonical case of three spatial dimensions, it was previously established that due to quantum buoyancy effects the box floats at some neutral point very close to the horizon. We find here that the significance of quantum buoyancy increases dramatically with the number $D$ of spatial dimensions. In particular, we find that the neutral (floating) point of the box lies near the horizon only if its length $b$ is large enough such that $b/b_C>F(D)$, where $b_C$ is the Compton length of the body and $F(D)\sim D^{D/2}\gg1$ for $D\gg1$. A consequence is that quantum buoyancy severely restricts our ability to deduce the universal entropy bound from the generalized second law of thermodynamics in higher-dimensional spacetimes with $D\gg1$. Nevertheless, we find that the universal entropy bound is always a sufficient condition for operation of the generalized second law in this type of gedanken experiments.Comment: 6 page

Finite Temperature Casimir Effect in Randall-Sundrum Models

The finite temperature Casimir effect for a scalar field in the bulk region of the two Randall-Sundrum models, RSI and RSII, is studied. We calculate the Casimir energy and the Casimir force for two parallel plates with separation $a$ on the visible brane in the RSI model. High-temperature and low-temperature cases are covered. Attractiveness versus repulsiveness of the temperature correction to the force is discussed in the typical special cases of Dirichlet-Dirichlet, Neumann-Neumann, and Dirichlet-Neumann boundary conditions at low temperature. The Abel-Plana summation formula is made use of, as this turns out to be most convenient. Some comments are made on the related contemporary literature.Comment: 33 pages latex, 2 figures. Some changes in the discussion. To appear in New J. Phy

Spatial averaging and apparent acceleration in inhomogeneous spaces

As an alternative to dark energy that explains the observed acceleration of the universe, it has been suggested that we may be at the center of an inhomogeneous isotropic universe described by a Lemaitre-Tolman-Bondi (LTB) solution of Einstein's field equations. To test this possibility, it is necessary to solve the null geodesics. In this paper we first give a detailed derivation of a fully analytical set of differential equations for the radial null geodesics as functions of the redshift in LTB models. As an application we use these equaions to show that a positive averaged acceleration $a_D$ obtained in LTB models through spatial averaging can be incompatible with cosmological observations. We provide examples of LTB models with positive $a_D$ which fail to reproduce the observed luminosity distance $D_L(z)$. Since the apparent cosmic acceleration $a^{FLRW}$ is obtained from fitting the observed luminosity distance to a FLRW model we conclude that in general a positive $a_D$ in LTB models does not imply a positive $a^{FLRW}$.Comment: 16 pages, 12 figures. Explicit derivation of the fully analytical null geodesic equations has been added. Published in GR

Radial asymptotics of Lemaitre-Tolman-Bondi dust models

We examine the radial asymptotic behavior of spherically symmetric Lemaitre-Tolman-Bondi dust models by looking at their covariant scalars along radial rays, which are spacelike geodesics parametrized by proper length $\ell$, orthogonal to the 4-velocity and to the orbits of SO(3). By introducing quasi-local scalars defined as integral functions along the rays, we obtain a complete and covariant representation of the models, leading to an initial value parametrization in which all scalars can be given by scaling laws depending on two metric scale factors and two basic initial value functions. Considering regular "open" LTB models whose space slices allow for a diverging $\ell$, we provide the conditions on the radial coordinate so that its asymptotic limit corresponds to the limit as $\ell\to\infty$. The "asymptotic state" is then defined as this limit, together with asymptotic series expansion around it, evaluated for all metric functions, covariant scalars (local and quasi-local) and their fluctuations. By looking at different sets of initial conditions, we examine and classify the asymptotic states of parabolic, hyperbolic and open elliptic models admitting a symmetry center. We show that in the radial direction the models can be asymptotic to any one of the following spacetimes: FLRW dust cosmologies with zero or negative spatial curvature, sections of Minkowski flat space (including Milne's space), sections of the Schwarzschild--Kruskal manifold or self--similar dust solutions.Comment: 44 pages (including a long appendix), 3 figures, IOP LaTeX style. Typos corrected and an important reference added. Accepted for publication in General Relativity and Gravitatio

An inhomogeneous alternative to dark energy?

Recently, there have been suggestions that the apparent accelerated expansion of the universe is not caused by repulsive gravitation due to dark energy, but is rather a result of inhomogeneities in the distribution of matter. In this work, we investigate the behaviour of a dust dominated inhomogeneous Lemaitre-Tolman-Bondi universe model, and confront it with various astrophysical observations. We find that such a model can easily explain the observed luminosity distance-redshift relation of supernovae without the need for dark energy, when the inhomogeneity is in the form of an underdense bubble centered near the observer. With the additional assumption that the universe outside the bubble is approximately described by a homogeneous Einstein-de Sitter model, we find that the position of the first CMB peak can be made to match the WMAP observations. Whether or not it is possible to reproduce the entire CMB angular power spectrum in an inhomogeneous model without dark energy, is still an open question.Comment: 8 pages (REVTeX4), 4 figures. v2: Minor changes to text plus added some references. Accepted for publication in PR

Do primordial Lithium abundances imply there's no Dark Energy?

Explaining the well established observation that the expansion rate of the universe is apparently accelerating is one of the defining scientific problems of our age. Within the standard model of cosmology, the repulsive 'dark energy' supposedly responsible has no explanation at a fundamental level, despite many varied attempts. A further important dilemma in the standard model is the Lithium problem, which is the substantial mismatch between the theoretical prediction for 7-Li from Big Bang Nucleosynthesis and the value that we observe today. This observation is one of the very few we have from along our past worldline as opposed to our past lightcone. By releasing the untested assumption that the universe is homogeneous on very large scales, both apparent acceleration and the Lithium problem can be easily accounted for as different aspects of cosmic inhomogeneity, without causing problems for other cosmological phenomena such as the cosmic microwave background. We illustrate this in the context of a void model.Comment: 14 pages, 4 figures. v2: minor rearrangements in the text, comments and references expanded, results unchange