Physics and cosmology in an inhomogeneous Universe

The aim of this paper is to check if the models with realistic inhomogeneous matter distribution and without cosmological constant can explain the dimming of the supernovae in such a way that it can be interpreted as an acceleration of the Universe. Employing the simplest inhomogeneous model, i.e. Lemaitre-Tolman model, this paper examines the impact of inhomogeneous matter distribution on light propagation. These analyses show that realistic matter fluctuations on small scal...

We study the evolution of linear perturbations in a Lema\^itre-Tolman-Bondi (LTB) void model with realistic cosmological initial conditions. Linear perturbation theory in LTB models is substantially more complicated than in standard Friedmann universes as the inhomogeneous background causes gauge-invariant perturbations to couple at first order. As shown by Clarkson et al. (2009), the evolution is constrained by a system of linear partial differential equations which need to ...

This work provides a general discussion of the spatially inhomogeneous Lema\^itre-Tolman-Bondi (LTB) cosmology, as well as its basic properties and many useful relevant quantities, such as the cosmological distances. We apply the concept of the single null geodesic to produce some simple analytical solutions for observational quantities such as the redshift. As an application of the single null geodesic technique, we carry out a fractal approach to the parabolic LTB model, co...

The existence of stars and galaxies reqires cosmological models with an inhomogeneous matter and radiation distribution. But in these models the initial singularity surface t_0(r) is in general homogeneous (independent of r). In this second paper of a series devoted to an inhomogeneous Big Bang singularity, we investigate the cosmic microwave background radiation (CMBR) dipole. A special Tolman-Bondi Universe is used to study the effect of a Big-Bang singularity, depending li...

This work examines a relativistic model for the observed inhomogeneities of the large scale structure where the hypothesis that this structure can be described as being a self-similar fractal system is advanced. The concept of hierarchical clustering is identified with a fractal distribution and the problems raised by the use of fractal ideas in a relativistic model are discussed, as well as their relations to the Copernican and Cosmological Principles. Voids, clusters and su...

The inverse problem with Lema\^itre-Tolman-Bondi (LTB) universe models is discussed. The LTB solution for the Einstein equations describes the spherically symmetric dust-filled spacetime. The LTB solution has two physical functional degrees of freedom of the radial coordinate. The inverse problem is constructing an LTB model requiring that the LTB model be consistent with selected important observational data. In this paper, we assume that the observer is at the center and co...

In this manuscript, we show that three fundamental building blocks are supporting the Cosmological Principle. The first of them states that there is a special frame in the universe where the spatial geometry is intrinsically homogeneous and isotropic. The second demands the existence of a fiducial observer to whom the Hubble parameter is isotropic. The last piece states that matter and radiation behave as a perfect fluid. We show that these three hypotheses give us the Friedm...

The approximate homogeneity of spatial sections of the Universe is well supported observationally, but the inhomogeneity of the spatial sections is even better supported. Here, we consider the implications of inhomogeneity in dust models for the connectedness of spatial sections at early times. We consider a non-global Lemaitre-Tolman-Bondi (LTB) model designed to match observations, a more general, heuristic model motivated by the former, and two specific, global LTB models....

The present talk summarizes the recently progressed state of a systematic re-evaluation of cosmological models that respect the presence of inhomogeneities. Emphasis is given to identifying the basic steps towards an effective (i.e. spatially averaged) description of structural evolution, also unfolding the various facets of a `smoothed--out' cosmology. We shall highlight some results obtained within Newtonian cosmology, discuss expansion laws in general relativity within a c...

The inhomogeneous distribution of matter in the non-linear regime of galaxies, clusters of galaxies and voids is described by an exact, spherically symmetric inhomogeneous solution of Einstein's gravitational field equations, corresponding to an under-dense void. The solution becomes the homogeneous and isotropic Einstein-de Sitter solution for a red shift $z > 10-20$, which describes the matter dominated CMB data with small inhomogeneities. A spatial volume averaging of phys...