Related papers: Relativistic rigid systems and the cosmic expansio…
There are many different formulations of relativistic elasticity. Most of them are only concerned with formal questions rather than questions regarding the PDE point of view. The aim of this thesis is to obtain various local existence…
The astronomical observations indicate that the universe expands with acceleration and it has a finite event horizon. The recent CMB observations confirm the universe is homogeneous, isotropic and asymptotically flat. The total…
One signature of an expanding universe is the time-variation of the cosmological abundances of its different components. For example, a radiation-dominated universe inevitably gives way to a matter-dominated universe, and critical moments…
The expansion of our universe, when followed backward in time, implies that it emerged from a phase of huge density, the big bang. These stages are so extreme that classical general relativity combined with matter theories is not able to…
We attempt to find new symmetries in the space-time structure, leading to a modified gravitation at large length scales, which provides the foundations of a quantum gravity at very low energies. This search begins by considering a unified…
A universe consisting of two interacting perfect fluids with the same 4-velocity is considered. A heuristic mean free time argument is used to show that the system as a whole cannot be perfect as well but neccessarily implies a nonvanishing…
For a general dark-energy equation of state, we estimate the maximum possible radius of massive structures that are not destabilized by the acceleration of the cosmological expansion. A comparison with known stable structures constrains the…
Using an approach that treats the Ricci scalar itself as a degree of freedom, we analyze the cosmological evolution within an f(R) model that has been proposed recently (exponential gravity) and that can be viable for explaining the…
Modifications to gravity can provide attractive alternatives to the dark components of the standard model of cosmology. These modifications to general relativity (GR) must be hidden at small scales where theory is well tested, and so one…
We explore the effects of background cosmology on large scale structures with non-spherical symmetry by using the concept of quasi-equilibrium which allows certain internal properties (e.g. angular velocity) of the bodies to change with…
It has been suggested that re-expressing relativity in terms of forces could provide fresh insights. The formalism developed for this purpose only applied to static, or conformally static, space-times. Here we extend it to arbitrary…
In Minkowski spacetime, we consider an isolated system made of two pointlike bodies interacting at a distance, in the nonradiative approximation. Our framework is the covariant and a priori Hamiltonian formalism of "predictive relativistic…
When dark matter structures form and equilibrate they have to release a significant amount of energy in order to obey the virial theorem. Since dark matter is believed to be unable to radiate, this implies that some of the accreted dark…
The expression of a time-dependent cosmological constant $\lambda \propto 1/t^2$ is interpreted as the energy density of a special type of the quaternionic field. The Lorenz-like force acting on the moving body in the presence of this…
The meaning of the expansion of the universe, or the `expansion of space,' is explored using two phenomena: the motion of a test particle against a homogeneous background and the cosmological redshift. Contrary to some expectations, a…
A brief summary of several topics in the study of gravitational many body problem is given. The discussion covers both static backgrounds (applicable to astrophysical systems) as well as clustering in an expanding background (relevant for…
A reference frame consists of: a reference space, a time scale and a spatial metric. The geometric structure induced by these objects in spacetime is developed. The existence of a class of spatial metrics that are rigid, have free mobility…
Starting from some relevant facts concerning the behaviour of the universe over large scale and time span, the analogy between the geometric approach of General Relativ- ity and the classical description of an elastic strained material…
We make the hypothesis that the velocity of light and the expansion of the universe are two aspects of one single concept connecting space and time in the expanding universe. We show that solving Friedman's equations with that…
We consider here a spherically symmetric but inhomogeneous universe filled with a massless scalar field. The model obeys two constraints. The first one is that the gradient of the scalar field is timelike everywhere. The second constraint…