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In some cosmological theories with varying constants there are anthropic reasons why the expansion of the universe must not be too {\it close} to flatness or the cosmological constant too close to zero. Using exact theories which…
A new model of nonlinear electrodynamics with dimensional parameters $\beta$ and $\gamma$ is proposed. The principles of causality and unitarity are studied. We show that a singularity of the electric field at the origin of charges is…
We refer to the classic definition of a singularity in Einstein's general relativity (based on geodesic incompletness) as well as to some other criteria to evaluate the nature of singularities in cosmology. We review what different…
In astro-ph/0601489, within the framework of the Einsteinian general relativity, we made the observation that if the universe is described by a spatially flat Friedmann-Robertson-Walker (FRW) cosmology with Einsteinian cosmological constant…
Four-dimensional Einstein's General Relativity is shown to arise from a gauge theory for the conformal group, SO(4,2). The theory is constructed from a topological dimensional reduction of the six-dimensional Euler density integrated over a…
In a previous work [1], it was speculated that the lack of homogeneity of the large-scale structure of the universe may be due to quantum fluctuations of space in the early universe. In [1], this was argued for a Friedmann-type universe for…
In creating his gravitational field equations Einstein unjustifiedly assumed that inertial mass, and its energy equivalent, is a source of gravity. Denying this assumption allows modifying the field equations to a form in which a positive…
Structure in the Universe is widely believed to have originated from quantum fluctuations during an early epoch of accelerated expansion. Yet, the patterns we observe today do not distinguish between quantum or classical primordial…
The big bang singularity could be understood as a breakdown of Einstein's General Relativity at very high energies. Adopting this viewpoint, other theories, that implement Einstein Cosmology at high energies, might solve the problem of the…
Singularity theorems demonstrate the inevitable breakdown of the concept of continuous, classical spacetime under highly general conditions. Quantum gravity is expected to intervene to avoid singularities and models so far hint towards…
The observable universe is fundamentally inhomogeneous and anisotropic. Quantum description of the generation of these inhomogeneities and anisotropies is ill-understood and unsatisfactory. After providing a brief account of the standard…
In this letter we will revise the steps followed by A. Einstein when he first wrote on cosmology from the point of view of the general theory of relativity. We will argue that his insightful line of thought leading to the introduction of…
Loop quantum cosmology is an application of recent developments for a non-perturbative and background independent quantization of gravity to a cosmological setting. Characteristic properties of the quantization such as discreteness of…
The universe has evolved to be a filamentary web of galaxies and large inter-galactic zones of space without matter. The Euclidian nature of the universe indicates that it is not a 3D manifold within space with an extra spatial dimension.…
We present a new class of complex instantons in the context of ekpyrotic cosmological theories. These instantons, which satisfy the "no-boundary" boundary conditions, describe the emergence of a classical, contracting universe out of…
A relativistic cosmological perturbation theory for the Friedmann-Lema\^itre-Robertson-Walker universe is presented that explains the masses and formation times of the first structures in our universe. First, it is shown that, without a…
One of the few firm predictions of string theory is the existence of a massless scalar field coupled to gravity, the dilaton. In its presence, the value of the fundamental constants of the universe, such as the fine-structure constant, will…
We discuss cosmological solutions for a diffeomorphism invariant gauge theory of the non-compact Lorentz group $SO(1,3)$. Besides the gauge bosons our model of pregeometry contains a vector field in the vector representation of $SO(1,3)$…
The topology of the universe is discussed in relation to the singularity problem. We explore the possibility that the initial state of the universe might have had a structure with 3-Klein bottle topology, which would lead to a model of a…
(abridged) Both fundamental constants that describe the laws of physics and cosmological parameters that determine the cosmic properties must fall within a range of values in order for the universe to develop astrophysical structures and…