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With the era of precision cosmology upon us, and upcoming surveys expected to further improve the precision of our observations below the percent level, ensuring the accuracy of our theoretical cosmological model is of the utmost…
We discuss the effect of curvature and matter inhomogeneities on the averaged scalar curvature of the present-day Universe. Motivated by studies of averaged inhomogeneous cosmologies, we contemplate on the question whether it is sensible to…
The current standard model of cosmology, the LambdaCDM model, is based on the homogeneous FLRW solutions of the Einstein equations to which some perturbations are added to account for the CMB features and structure formation at large…
If general relativity (GR) describes the expansion of the Universe, the observed cosmic acceleration implies the existence of a `dark energy'. However, while the Universe is on average homogeneous on large scales, it is inhomogeneous on…
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…
The effective evolution of an inhomogeneous universe model in any theory of gravitation may be described in terms of spatially averaged variables. In Einstein's theory, restricting attention to scalar variables, this evolution can be…
We perform large-scale cosmological simulations that solve Einstein's equations directly via numerical relativity. Starting with initial conditions sampled from the cosmic microwave background, we track the emergence of a cosmic web without…
The apparent accelerating expansion of the Universe is forcing us to examine the foundational aspects of the standard model of cosmology -- in particular, the fact that dark energy is a direct consequence of the homogeneity assumption. We…
The backreaction of structure formation influences the cosmological evolution equation for the homogenous and isotropic average metric. In a cold dark matter universe this effect leads only to small corrections unless a substantial fraction…
It is commonly stated that we have entered the era of precision cosmology in which a number of important observations have reached a degree of precision, and a level of agreement with theory, that is comparable with many Earth-based physics…
A system of effective Einstein equations for spatially averaged scalar variables of inhomogeneous cosmological models can be solved by providing a `cosmic equation of state'. Recent efforts to explain Dark Energy focus on `backreaction…
These lecture notes review the theoretical problems associated with coarse-graining the observed inhomogeneous structure of the universe at late epochs, of describing average cosmic evolution in the presence of growing inhomogeneity, and of…
Over the last decades, observations with increasing quality have revolutionized our understanding of the general properties of the Universe. Questions posed for millenia by mankind about the origin, evolution and structure of the cosmos…
There is now strong evidence that the current energy density of the Universe is dominated by dark energy with an equation of state w<-1/3, which is causing accelerated expansion. The build-up of structure within such Universes is subject to…
Assuming the universe is spatially homogeneous on the largest scales lays the foundation for almost all cosmology. This idea is based on the Copernican principle, that we are not at a particularly special place in the universe.…
The standard model of cosmology with postulated dark energy and dark matter sources may be considered as a fairly successful fitting model to observational data. However, this model leaves the question of the physical origin of these dark…
Kinematical and dynamical properties of a generic inhomogeneous cosmological model, spatially averaged with respect to free-falling (generalized fundamental) observers, are investigated for the matter model irrotational dust. Paraphrasing a…
The current expansion of the Universe has been observed to be accelerating, and the widely accepted spatially-flat concordance model of general relativistic cosmology attributes this phenomenon to a constant dark energy, a cosmological…
A mildly inhomogeneous universe with a cosmological constant may look like it contains evolving dark energy. We show that could be the case by modelling the inhomogeneities and their effects in three different ways: as clumped matter…
Explanations of the late-time cosmic acceleration within the framework of general relativity are plagued by difficulties. General relativistic models are mostly based on a dark energy field with fine-tuned, unnatural properties. There is a…