Related papers: Einstein-Vlasov Calculations of Structure Formatio…
In cosmology numerical simulations of structure formation are now of central importance, as they are the sole instrument for providing detailed predictions of current cosmological models for a whole class of important constraining…
We present extensions of the treatment contained in our recent paper on nonlocal Newtonian cosmology [C. Chicone and B. Mashhoon, J. Math. Phys. 57, 072501 (2016)]. That is, the implications of the recent nonlocal generalization of…
We discuss the relation between the output of Newtonian N-body simulations on scales that approach or exceed the particle horizon to the description of General Relativity. At leading order, the Zeldovich approximation is correct on large…
Idealizing matter as a pressureless fluid and representing its motion by a peculiar--velocity field superimposed on a homogeneous and isotropic Hubble expansion, we apply (Lagrangian) spatial averaging on an arbitrary domain $\cal D$ to the…
N-Body simulations are a very important tool in the study of formation of large scale structures. Much of the progress in understanding the physics of galaxy formation and comparison with observations would not have been possible without…
It is shown that a first-order relativistic perturbation theory for the open, flat or closed Friedmann-Lemaitre-Robertson-Walker universe admits one, and only one, gauge-invariant quantity which describes the perturbation to the energy…
We present the first calculation of an intrinsically relativistic quantity in fully non-linear cosmolog- ical large-scale structure studies. Traditionally, non-linear structure formation in standard {\Lambda}CDM cosmology is studied using…
The Einstein equations for an inhomogeneous irrotational dust universe are analysed. A set of mild assumptions, all of which are shared by the standard FLRW type scenarios, results in a model that depends only on the distribution of scalar…
The non-linearity of Einstein's equations makes it possible for small-scale matter inhomogeneities to affect the Universe at cosmological distances. We study the size of such effects using a simple heuristic model that captures the most…
I consider the growth of inhomogeneities in a low-density baryonic, vacuum energy-dominated universe in the context of modified Newtonian dynamics (MOND). I first write down a two-field Langrangian-based theory of MOND (non-relativistic),…
We study the inhomogeneous cosmological evolution of the Newtonian gravitational 'constant' G in the framework of scalar-tensor theories. We investigate the differences that arise between the evolution of G in the background universes and…
General relativity manifests very similar equations in different regimes, notably in large scale cosmological perturbation theory, non-linear cosmological structure formation, and in weak field galactic dynamics. The same is not necessarily…
Spherically symmetric, static model of the cosmological voids is constructed in the framework of the Tolman-Oppenheimer-Volkov equation with the cosmological constant. Extension of the Tooper result (dimensionless form of the TOV equation)…
We numerically investigate the dynamics near black hole formation of solutions to the Einstein--Vlasov system in axisymmetry. Our results are obtained using a particle-in-cell and finite difference code based on the $(2+1)+1$ formulation of…
Numerical N-body simulations of large scale structure formation in the universe are based on Newtonian gravity. However, according to our current understanding, the most correct theory of gravity is general relativity. It is therefore…
Possibilities emerging out of the dynamical evolutions of collapsing systems are addressed in this thesis through analytical investigations of the highly non-linear Einstein Field Equations. Studies of exact solutions and their properties,…
We present $N$-body simulations in which either all, or a fraction of, the cold dark matter decays non-relativistically to a relativistic, non-interacting dark radiation component. All effects from radiation and general relativity are…
An important open question in cosmology is the degree to which the Friedmann-Lemaitre-Robertson-Walker (FLRW) solutions of Einstein's equations are able to model the large-scale behaviour of the locally inhomogeneous observable universe. We…
We establish the existence of a wide class of inhomogeneous relativistic solutions to the Einstein-Euler equations that are well approximated on cosmological scales by solutions of Newtonian gravity. Error estimates measuring the difference…
A new method for constructing exact inhomogeneous universes is presented, that allows variation in 3 dimensions. The resulting spacetime may be statistically uniform on average, or have random, non-repeating variation. The construction…