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The notion of vacuum fluctuations of the gravitational field plays important role in cosmology. The strong variable gravitational field of the very early Universe amplifies these fluctuations and transforms them into macroscopical…
Modern cosmological observations allow us to study in great detail the evolution and history of the large scale structure hierarchy. The fundamental problem of accurate constraints on the cosmological parameters, within a given cosmological…
I discuss some aspects of the use of computers in Relativity, Astrophysics and Cosmology. For each section I provide two examples representative of the field, including gravitational collapse, black hole imagery, supernovae explosions,…
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…
In an undulant universe, cosmic expansion is characterized by alternating periods of acceleration and deceleration. We examine cosmologies in which the dark-energy equation of state varies periodically with the number of e-foldings of the…
These lecture notes discuss several topics in the physics of cosmic structure formation starting from the evolution of small-amplitude fluctuations in the radiation-dominated era. The topics include relativistic cosmological perturbation…
With the beginning of the XXIst century, a physical model of our Universe, usually called the Standard Cosmological Model (SCM), is reaching an important level of consolidation, based on accurate astrophysical data and also on theoretical…
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…
The analysis of the dynamics of radial movement in different reference frames used in cosmology is made. Use of different frames leads to the difference in inertial forces resulting in different observable effects. The important effect is…
Modeling galaxy formation in a cosmological context presents one of the greatest challenges in astrophysics today, due to the vast range of scales and numerous physical processes involved. Here we review the current status of models that…
Dark matter has been introduced to explain many independent gravitational effects at different astronomical scales, in galaxies, groups of galaxies, clusters, superclusters and even across the full horizon. This review describes the…
We present a class of general prolate and oblate spheroidal spacetimes for the description of cosmic structures in the Universe. They are exact geometries which represent, in an appropriated way, the imbedding of spheroidal matter-energy…
The observational evidence for the recent acceleration of the universe demonstrates that canonical theories of cosmology and particle physics are incomplete (or possibly incorrect) and that new physics is out there, waiting to be…
General relativity marked the beginning of modern cosmology and it has since been at the centre of many of the key developments in this field. In the present review, we discuss the general-relativistic dynamics and perturbations of the…
We consider a principal problem, that of the possible dominating role of self-consistent gravitational interaction in the formation of cosmic structures: voids and their walls in the local Universe. It is in the context of the Hubble…
The impact of a fast decaying component of mass-energy, that decreases faster than radiation with the increase of the scale factor, on the evolution of the universe is studied using a hydrodynamic approach. Proceeding from the Hamiltonian…
Recent advances in our understanding of the Universe have revolutionized our view of its structure, composition and evolution. However, these new ideas have not necessarily been used to improve the teaching of introductory astronomy…
A range of cosmological observations demonstrate an accelerated expansion of the Universe, and the most likely explanation of this phenomenon is a cosmological constant. Given the importance of understanding the underlying physics, it is…
We study the cosmological stability of a class of theories with a dynamical preferred frame. For a range of actions, we find cosmological solutions which are compatible with observations of the recent history of the Universe: a matter…
The theory of cosmological perturbations has become a cornerstone of modern quantitative cosmology since it is the framework which provides the link between the models of the very early Universe such as the inflationary Universe scenario…