Related papers: Discrete Newtonian Cosmology: Perturbations
The present paper outlines theoretical principles of the post-Newtonian mechanics in the expanding universe. It is based upon the gauge-invariant theory of the Lagrangian perturbations of cosmological manifold caused by an isolated…
We study a general relativistic particle action obtained by incorporating the Hamiltonian constraints into the formalism as a toy model for general relativity and string theory. We show how a non-vanishing cosmological constant and a…
We develop the canonical formalism for a system of $N$ bodies in lineal gravity and obtain exact solutions to the equations of motion for N=2. The determining equation of the Hamiltonian is derived in the form of a transcendental equation,…
We study the complete cosmological evolution of dark matter (DM) density fluctuations for DM particles that decoupled being ultrarelativistic during the radiation dominated era which is the case of keV scale warm DM (WDM). The new framework…
The cosmological constant and its phenomenology remain among the greatest puzzles in theoretical physics. We review how modifications of Einstein's general relativity could alleviate the different problems associated with it that result…
We study a rotating and expanding, Godel type metric, originally considered by Korotkii and Obukhov, showing that, in the limit of large times and nearby distances, it reduces to the open metric of Friedmann. In the epochs when radiation or…
The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple…
The dynamical realisation of the equation of state $p +\rho =0$ is studied. A non-pathological dynamics for the perturbations of such a system mimicking a dynamical cosmological constant (DCC) requires to go beyond the perfect fluid…
The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple…
In a homogeneous and isotropic universe with non-zero spatial curvature we consider the effects of gravitational particle production in the dynamics of the universe. We show that the dynamics of the universe in such a background is…
Gravitation is described in the context of a dilatonic theory that is conformally related to general relativity. All dimensionless ratios of fundamental dimensional quantities, e.g. particle masses and the Planck mass, as well as the…
We present a systematic treatment of the linear theory of scalar gravitational perturbations in the synchronous gauge and the conformal Newtonian (or longitudinal) gauge. We first derive the transformation law relating the two gauges. We…
This paper summarises a number of new, potentially significant, results, obtained recently by the author and his collaborators, which impact on various issues related to the gravitational N-body problem, both Newtonianly and in the context…
In this paper we consider a Vlasov or collisionless Boltzmann equation describing the dynamics of planetary rings. We propose a simple physical model, where the particles of the rings move under the gravitational Newtonian potential of two…
We consider systems of ODEs that describe the dynamics of particles. Each particle satisfies a Newton law (including the acceleration term) where the force is created by the interactions with the other particles and with a periodic…
The recently introduced consistent discrete lattice formulation of canonical general relativity produces a discrete theory that is constraint-free. This immediately allows to overcome several of the traditional obstacles posed by the…
The theory of cosmological perturbations is extended to spacetimes displaying isotropic expansion but anisotropic curvature. The perturbed Einstein equation and Boltzmann equations for massless and massive particles are derived in a general…
According to observations, in our Universe for gravitational phenomena in a Newtonian approximation the Newtonian non-modified relations are valid. The Friedmann equations of universe dynamics describe infinite number of relativistic…
Although the cosmological perturbations with inverse-volume corrections from loop quantum cosmology have been studied using the anomaly-free algebra approach in much of the literature, there still remains an important issue that some…
A generalization to the theory of massive gravity is presented which includes three dynamical metrics. It is shown that at the linear level, the theory predicts a massless spin-2 field which is decoupled from the other two gravitons which…