FC - DF | Dissertações de Mestrado e Teses de Doutoramento
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Browsing FC - DF | Dissertações de Mestrado e Teses de Doutoramento by advisor "Bouhmadi Lopez, Mariam"
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- Astrophysical and cosmological doomsdaysPublication . Tavakoli, Yaser; Moniz, Paulo Rodrigues Lima Vargas; Bouhmadi Lopez, MariamIn 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.
- The recent acceleration of the UniversePublication . Albarran Payo, Imanol; Bouhmadi Lopez, Mariam; Marto, João Pedro de JesusThe present thesis is aimed to disclose three genuine phantom Dark Energy (DE) models where each of them induce a particular cosmic doomsday. We have named these models as model A, model B and model C, while the corresponding induced cosmic events are known as Big Rip (BR), Little Rip (LR) and Little Sibling of the Big Rip (LS), respectively. We regard a BR as a true singularity since it takes place at a finite cosmic time, while we have coined LR and LS as abrupt events, since they occur at infinite cosmic time. Nevertheless, it is well known that in such abrupt events sooner or later all the bound structures would unavoidably torn away, and therefore, the Universe would face a total destruction at a finite cosmic time. On the one side, we have addressed the background phenomenology and the first order cosmological perturbations for the phantom DE models above mentioned. In addition, we have made use of the widely known ΛCDM model as a guideline to measure deviations among the models. Given that a DE content is present, we avoid the associated instabilities at the perturbative level by applying the method of DE pressure decomposition in its adiabatic and non‐adiabatic contributions. We compute, by means of numerical methods, the evolution of the perturbed quantities for a Universe filled with radiation, matter and DE. Such computations are carried from well inside the radiation dominated era to the far future. Then, we predict the current matter power spectrum and fσ8 growth rate for each model. The latter mentioned observable quantity is compared with the current observational data in order to find footprints that could allow us to distinguish between the mentioned models. For the sake of completeness, we have fitted observationally these phantom DE models together with ΛCDM in order to constrain the parameters characterising the models. On the one hand, we have found that despite that ΛCDM still gives the best fit, it is closely followed by the models studied in the present thesis. On the other hand, we have found that these genuine phantom models induce a sign switch of the gravitational potential at very large scale factors. This fact could be understood as gravity becoming effectively repulsive in the far future. Finally, we have studied the effects of DE speed of sound on the perturbations. On the other side, it is expected that quantum effects will become important when the Universe approaches a future cosmic singularity, which is the case of those events addressed in the present thesis. Unfortunately, we have not yet a consistent theory of quantum gravity to deal with the most dramatic effects that would take place at the end of the Universe. It is expected that such a fundamental quantum theory of gravity will naturally avoid those singularities present in the classical theory of General Relativity (GR). We have rather addressed the issue of cosmological singularity avoidance within the context of a quantum approach. The quantisation is carried via Wheeler‐DeWitt (WDW) equation and imposing the DeWitt (DW) boundary condition, i.e. the wave function vanishes close to the singularity. We have analysed each model by considering different factor orderings and solving the WDW equation for a DE content given by (i), a perfect fluid, and (ii), a scalar field. In addition, we have addressed these phantom models in the context of the Eddington‐inspired‐Born‐Infeld (EiBI) modified theory of gravity and applied the same quantisation methods above mentioned to analyse the avoidance of singularities from a quantum point of view. Therefore, this thesis is divided in two main parts, a classical part, where we present the back-ground and perturbations of three genuine phantom models, and a second part, where we address the avoidance of singularities induced by such models from a quantum point of view. Given that UBI allows to present the thesis as an introduction, a set of chapters based on the published works during the PhD and the conclusions, we have followed mainly this format.