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 Lemaître-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.

We investigate f (R) theories of gravity within the Palatini approach and show how one can determine the expansion history, H(a), for an arbitrary choice of f (R). As an example, we consider cosmological constraints on such theories arising from the supernova type Ia, large-scale structure formation, and cosmic microwave background observations. We find that the best fit to the data is a nonnull leading order correction to the Einstein gravity. However, the current data exhibits no significant trend toward such corrections compared to the concordance ΛCDM model. Our results show that the oft-considered 1/R models are not compatible with the data. The results demonstrate that background expansion alone can act as a good discriminator between modified gravity models when multiple data sets are used.

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.

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.

Abstract. 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 Lemaître-Tolman-Bondi universe models. We show that they do not permit accelerated cosmic expansion.