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Quantum gravity is likely the deepest problem facing current physics. While traditionally associated with short distance nonrenormalizability, it is evident that the long distance problem of unitarity, arising at high energies with black…
We introduce the set of constraints the wave function of the Universe has to satisfy in order to describe an Universe undergoing through the process of spontaneous breaking of supersymmetry and discuss the way this may lead to the emergence…
In the standard cosmological theory one uses the Einstein concepts of space and time as were originally introduced for the special theory of relativity and the general relativity theory. According to this approach all physical quantities…
This thesis focuses on modifications on Einstein's theory of General Relativity, which could explain the current problems in gravitation and cosmology. More specifically, modifications of the affine structure of the spacetime, which is the…
An alternative approach to Einstein's theory of General Relativity (GR) is reviewed, which is motivated by a range of serious theoretical issues inflicting the theory, such as the cosmological constant problem, presence of non-Machian…
A central theme in cosmology is the perplexing fact that the Universe is undergoing an accelerating expansion. The latter, one of the most important and challenging current problems in cosmology, represents a new imbalance in the governing…
We survey a variety of cosmological problems where the issue of generality has arisen. This is aimed at providing a wider context for many claims and deductions made when philosophers of science choose cosmological problems for…
Modern astrophysical and cosmological models are plagued with two severe theoretical difficulties, namely, the dark energy and the dark matter problems. Relative to the former, high-precision observational data have confirmed with startling…
Quantum gravity may remove classical space-time singularities and thus reveal what a universe at and before the big bang could be like. In loop quantum cosmology, an exactly solvable model is available which allows one to address precise…
The generalized second law can be used to prove a singularity theorem, by generalizing the notion of a trapped surface to quantum situations. Like Penrose's original singularity theorem, it implies that spacetime is null geodesically…
It is often said that in general relativity time does not exist. This is because the Einstein equations generate motion in time that is a symmetry of the theory, not true time evolution. In quantum gravity, the timelessness of general…
Is there a number for every bit of spacetime, or is spacetime smooth like the real line? The ultimate fate of a quantum theory of gravity might depend on it. The troublesome infinities of quantum gravity can be cured by assuming that…
Spacetime singularities have been discovered which are physically much weaker than those predicted by the classical singularity theorems. Geodesics evolve through them and they only display infinities in the derivatives of their curvature…
The black hole area theorem suggests that classical general relativity is the thermodynamic limit of a quantum statistics. The degrees of freedom of the statistical theory cannot be the spacetime metric. We argue that the statistical theory…
Familiar textbook quantum mechanics assumes a fixed background spacetime to define states on spacelike surfaces and their unitary evolution between them. Quantum theory has changed as our conceptions of space and time have evolved. But…
Einstein's general theory of relativity is the standard theory of gravity, especially where the needs of astronomy, astrophysics, cosmology and fundamental physics are concerned. As such, this theory is used for many practical purposes…
Numerical relativity is an essential tool for solving Einstein's equations of general relativity for dynamical systems characterized by high velocities and strong gravitational fields. The implementation of new algorithms that can solve…
The possibility of avoiding the big bang singularity by means of a generalized uncertainty principle is investigated. In relation with this matter, the statistical mechanics of a free-particle system obeying the generalized uncertainty…
A panoramic view, preceded by a short background of Newtonian mechanics and Maxwellian electrodynamics, is offered on the extent of how Einstein's space-time geometry, believed to be central to an understanding of the structure of the…
Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…