| Name: | Description: | Size: | Format: | |
|---|---|---|---|---|
| Documento principal | 2.66 MB | Adobe PDF |
Authors
Abstract(s)
In this dissertation we study two well known gravitational scenarios in which singularities
may appear. The first scenario can be brought in by the final state of gravitational collapse
(the singularity that is found, e.g., inside the event horizon of every black hole or,
if no trapped surface is formed, as a naked singularity instead). The second scenario is
the one corresponding to singularities that may appear at the late time evolution of the
universe.
In the context of gravitational collapse, we study a homogeneous spherically symmetric
space-time whose matter content includes a scalar field. We investigate a particular class
of such space-time, with a tachyon field and a barotropic fluid being present. By making
use of the specific kinematical features of the tachyon, which are rather different from a
standard scalar field, we establish several types of asymptotic behavior that our matter
content induces. Employing a dynamical system analysis, complemented by a thorough
numerical study, we find classical solutions corresponding to a naked singularity or a black
hole formation. Furthermore, we find a subset where the fluid and tachyon participate
in an interesting tracking behaviour, depending on the initial conditions for the energy
densities of the tachyon field and barotropic fluid.
It seems reasonable that the singularity indicates that the classical theory we use for
gravitational collapse (general relativity) cannot be trusted when the space-time curvature
becomes very large; quantum effects cannot be ignored. We therefore investigate,
in a semiclassical manner, loop quantum gravity (LQG) induced effects on the fate of the
classical singularities that arise at the final state of the gravitational collapse. We study
the semiclassical interior of a spherically symmetric space-time with a tachyon field and
barotropic fluid as matter content. We show how, due to two different types of corrections,
namely “inverse triad” and “holonomy”, classical singularities can be removed. By
employing an inverse triad correction, we obtain, for a semiclassical description, several
classes of analytical as well as numerical solutions. We identify a subset whose behavior
corresponds to an outward flux of energy, thus avoiding either a naked singularity
or a black hole formation. Within a holonomy correction, we obtain the semiclassical
counterpart of our classical solutions for the general relativistic collapse. We show that
classical singularity is resolved and replaced by a bounce. By employing a phase space
analysis in the semiclassical regime, we find that there is no stable fixed point solution,
hence no singular back hole neither naked singularities. In the context of the dark energy cosmology, we study the status of dark energy late
time singularities. We employ several models of dark energy to investigate whether they
remove or appease the classical singularities. In the first model we consider a Dvali-
Gabadadze-Porrati (DGP) brane-world model that has infra-red (IR) modifications through
an induced gravity term. It models our 4-dimensional world as a Friedmann-Lemaître-
Robertson-Walker (FLRW) brane embedded in a Minkowski bulk. A Gauss-Bonnet (GB)
term is provided for the bulk action whose higher order curvature terms modify gravity
at high energy (with ultra violet (UV) effects). Furthermore, a phantom matter is present
on the brane which constitutes the dark energy component of our universe. It is shown
that a combination of IR and UV modifications to general relativity replaces a big rip
singularity by a sudden singularity at late times.
Another model we consider herein to describe the origin of dark energy is the generalised
running vacuum energy (GRVE) model. The Friedmann equation of the GRVE model looks
much similar to that of a homogeneous and isotropic universe filled with an holographic
Ricci dark energy (HRDE) component. We study the late time behaviour of the universe
in the presence of these two models for dark energy. Despite the analogy between these
two models, it turns out that one of them, a GRVE, is singularity-free in the future while
the other, the HRDE, is not. Indeed, a universe filled with an HRDE component can hit, for
example, a big rip singularity. We clarify this issue by solving analytically the Friedmann
equation for both models and analyzing the role played by the local conservation of the
energy density of the different components filling the universe. In addition, we point
out that in some particular cases the HRDE, when endowed with a negative cosmological
constant and in the absence of an explicit dark matter component, can mimic dark matter
and explain the late time cosmic acceleration of the universe through an asymptotically
de Sitter universe.
Description
Keywords
Relatividade geral Singularidade gravitacional Granitação quântica Energia escura Cosmologia quântica Brana-mundo