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

The supernova Hubble diagram for off-center observers in a spherically symmetric inhomogeneous universe

We have previously shown that spherically symmetric, inhomogeneous universe models can explain both the supernova data and the location of the first peak in the CMB spectrum without resorting to dark energy. In this work, we investigate whether it is possible to get an even better fit to the supernova data by allowing the observer to be positioned away from the origin in the spherically symmetric coordinate system. In such a scenario, the observer sees an anisotropic relation between redshifts and the luminosity distances of supernovae. The level of anisotropy allowed by the data will then constrain how far away from the origin the observer can be located, and possibly even allow for a better fit. Our analysis shows that the fit is indeed improved, but not by a significant amount. Furthermore, it shows that the supernova data do not place a rigorous constraint on how far off-center the observer can be located.Comment: 7 pages (REVTeX4), 5 figure

Gradient expansion(s) and dark energy

Motivated by recent claims stating that the acceleration of the present Universe is due to fluctuations with wavelength larger than the Hubble radius, we present a general analysis of various perturbative solutions of fully inhomogeneous Einstein equations supplemented by a perfect fluid. The equivalence of formally different gradient expansions is demonstrated. If the barotropic index vanishes, the deceleration parameter is always positive semi-definite.Comment: 17 pages, no figure

Cosmic Acceleration Driven by Mirage Inhomogeneities

A cosmological model based on an inhomogeneous D3-brane moving in an AdS_5 X S_5 bulk is introduced. Although there is no special points in the bulk, the brane Universe has a center and is isotropic around it. The model has an accelerating expansion and its effective cosmological constant is inversely proportional to the distance from the center, giving a possible geometrical origin for the smallness of a present-day cosmological constant. Besides, if our model is considered as an alternative of early time acceleration, it is shown that the early stage accelerating phase ends in a dust dominated FRW homogeneous Universe. Mirage-driven acceleration thus provides a dark matter component for the brane Universe final state. We finally show that the model fulfills the current constraints on inhomogeneities.Comment: 14 pages, 1 figure, IOP style. v2, changed style, minor corrections, references added, version accepted in Class. Quant. Gra

Cosmological perturbations in the Palatini formulation of modified gravity

Cosmology in extended theories of gravity is considered assuming the Palatini variational principle, for which the metric and connection are independent variables. The field equations are derived to linear order in perturbations about the homogeneous and isotropic but possibly spatially curved background. The results are presented in a unified form applicable to a broad class of gravity theories allowing arbitrary scalar-tensor couplings and nonlinear dependence on the Ricci scalar in the gravitational action. The gauge-ready formalism exploited here makes it possible to obtain the equations immediately in any of the commonly used gauges. Of the three type of perturbations, the main attention is on the scalar modes responsible for the cosmic large-scale structure. Evolution equations are derived for perturbations in a late universe filled with cold dark matter and accelerated by curvature corrections. Such corrections are found to induce effective pressure gradients which are problematical in the formation of large-scale structure. This is demonstrated by analytic solutions in a particular case. A physical equivalence between scalar-tensor theories in metric and in Palatini formalisms is pointed out.Comment: 14 pages; the published version (+ an appendix). Corrected typos in eqs. 30,33 and B

The Effect of Large-Scale Inhomogeneities on the Luminosity Distance

We study the form of the luminosity distance as a function of redshift in the presence of large scale inhomogeneities, with sizes of order 10 Mpc or larger. We approximate the Universe through the Swiss-cheese model, with each spherical region described by the Tolman-Bondi metric. We study the propagation of light beams in this background, assuming that the locations of the source and the observer are random. We derive the optical equations for the evolution of the beam area and shear. Through their integration we determine the configurations that can lead to an increase of the luminosity distance relative to the homogeneous cosmology. We find that this can be achieved if the Universe is composed of spherical void-like regions, with matter concentrated near their surface. For inhomogeneities consistent with the observed large scale structure, the relative increase of the luminosity distance is of the order of a few percent at redshifts near 1, and falls short of explaining the substantial increase required by the supernova data. On the other hand, the effect we describe is important for the correct determination of the energy content of the Universe from observations.Comment: 27 pages, 5 figures Revised version. References added. Conclusions clarifie

On globally static and stationary cosmologies with or without a cosmological constant and the Dark Energy problem

In the framework of spatially averaged inhomogeneous cosmologies in classical General Relativity, effective Einstein equations govern the regional and the global dynamics of averaged scalar variables of cosmological models. A particular solution may be characterized by a cosmic equation of state. In this paper it is pointed out that a globally static averaged dust model is conceivable without employing a compensating cosmological constant. Much in the spirit of Einstein's original model we discuss consequences for the global, but also for the regional properties of this cosmology. We then consider the wider class of globally stationary cosmologies that are conceivable in the presented framework. All these models are based on exact solutions of the averaged Einstein equations and provide examples of cosmologies in an out-of-equilibrium state, which we characterize by an information-theoretical measure. It is shown that such cosmologies preserve high-magnitude kinematical fluctuations and so tend to maintain their global properties. The same is true for a $\Lambda-$driven cosmos in such a state despite of exponential expansion. We outline relations to inflationary scenarios, and put the Dark Energy problem into perspective. Here, it is argued, on the grounds of the discussed cosmologies, that a classical explanation of Dark Energy through backreaction effects is theoretically conceivable, if the matter-dominated Universe emerged from a non-perturbative state in the vicinity of the stationary solution. We also discuss a number of caveats that furnish strong counter arguments in the framework of structure formation in a perturbed Friedmannian model.Comment: 33 pages, matches published version in Class. Quant. Gra

Can a dust dominated universe have accelerated expansion?

Recently, there has been suggestions that the apparent accelerated expansion of the universe is due not to a cosmological constant, but rather to inhomogeneities in the distribution of matter. In this work, we investigate a specific class of inhomogeneous models that can be solved analytically, namely the dust-dominated Lemaitre-Tolman-Bondi universe models. We show that they do not permit accelerated cosmic expansion.Comment: 9 pages, 1 figure. v3: Paper shortened and updated. References added. v4: Minor LATEX problem fixed. Submitted to JCA

On cosmic acceleration without dark energy

We elaborate on the proposal that the observed acceleration of the Universe is the result of the backreaction of cosmological perturbations, rather than the effect of a negative-pressure dark-energy fluid or a modification of general relativity. Through the effective Friedmann equations describing an inhomogeneous Universe after smoothing, we demonstrate that acceleration in our local Hubble patch is possible even if fluid elements do not individually undergo accelerated expansion. This invalidates the no-go theorem that there can be no acceleration in our local Hubble patch if the Universe only contains irrotational dust. We then study perturbatively the time behavior of general-relativistic cosmological perturbations, applying, where possible, the renormalization group to regularize the dynamics. We show that an instability occurs in the perturbative expansion involving sub-Hubble modes. Whether this is an indication that acceleration in our Hubble patch originates from the backreaction of cosmological perturbations on observable scales requires a fully non-perturbative approach.Comment: 33 pages, LaTeX file. Revised to match the final version accepted for publication in NJ

Accelerated expansion from structure formation

We discuss the physics of backreaction-driven accelerated expansion. Using the exact equations for the behaviour of averages in dust universes, we explain how large-scale smoothness does not imply that the effect of inhomogeneity and anisotropy on the expansion rate is small. We demonstrate with an analytical toy model how gravitational collapse can lead to acceleration. We find that the conjecture of the accelerated expansion being due to structure formation is in agreement with the general observational picture of structures in the universe, and more quantitative work is needed to make a detailed comparison.Comment: 44 pages, 1 figure. Expanded treatment of topics from the Gravity Research Foundation contest essay astro-ph/0605632. v2: Added references, clarified wordings. v3: Published version. Minor changes and corrections, added a referenc