Related papers: Cosmic dimensions
The continuum of real numbers has served well as a model for physical space in mechanics and field theories. However it is a well-motivated and popular idea that at the fundamental Planck scale the combination of gravitational and quantum…
We construct infinite dimensional families of non-singular stationary space times, solutions of the vacuum Einstein equations with a negative cosmological constant.
In the past several decades, multiple cosmological theories that are based on the contention that the Universe has a major axis have been proposed. Such theories can be based on the geometry of the Universe, or multiverse theories such as…
Higher dimensional supersymmetric quantum mechanics is studied. General properties of the two dimensional case are presented. For three spatial dimesions or higher, a spin structure is shown to arise naturally from the nonrelativistic…
The present study introduces the notions of statistical convergence of order $\alpha$ and strong $p-$ Ces\`{a}ro summability of order $\alpha$ in partial metric spaces. Also, we examine the inclusion relations between these concepts. In…
The principles of General Relativity allow for a non-vanishing cosmological constant, which can possibly be interpreted at least partially in terms of quantum-fluctuations of matter fields. Depending on sign and magnitude it can cause…
We examine the cosmology of the two recently proposed scenarios for a five dimensional universe with localized gravity. We find that the scenario with a non-compact fifth dimension is potentially viable, while the scenario which might solve…
Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We…
The two closely related Lorentz-invariant partial orders of space-time are distinguished with respect to the existence of antichain cutsets and the possibility of grading. World lines of particles with or without mass are the maximal chains…
In this thesis the cosmological constant is investigated from two points of view. First, we study the influence of a time-dependent cosmological constant on the late-time expansion of the universe. Thereby, we consider several combinations…
In order to resolve the hierarchy problem, large extra dimensions have been introduced, and it has been suggested that the size of extra dimensions is sub-millimeter. On the other hand, we assume in this paper that the cosmological constant…
A physical theory of the world is presented under the unifying principle that all of nature is laid out before us and experienced through the passage of time. The one-dimensional progression in time is opened out into a multi-dimensional…
Higher-dimensional theories of the kind which may unify gravitation with particle physics can lead to significant modifications of general relativity. In five dimensions, the vacuum becomes non-standard, and the Weak Equivalence Principle…
I discuss a set of strong, but probabilistically intelligible, axioms from which one can {\em almost} derive the appratus of finite dimensional quantum theory. Stated informally, these require that systems appear completely classical as…
We consider a two-dimensional model of gravity with the cosmological constant as a dynamical variable. The effective cosmological constant is derived when the universe has no initial boundary. It turns out to be extremely small if the…
Copernicus realised we were not at the centre of the universe. A universe made finite by topological identifications introduces a new Copernican consideration: while we may not be at the geometric centre of the universe, some galaxy could…
We investigate a sequence of quadratic topological terms of the Chern-Simons type in different spacetime dimensions, related by dimensional compactification and sharing the properties of topological mass generation and statistical…
We provide detailed evidence for the claim that nonperturbative quantum gravity, defined through state sums of causal triangulated geometries, possesses a large-scale limit in which the dimension of spacetime is four and the dynamics of the…
A `whole-part' theory is developed for a set of finite quantum systems $\Sigma (n)$ with variables in ${\mathbb Z}(n)$. The partial order `subsystem' is defined, by embedding various attributes of the system $\Sigma (m)$ (quantum states,…
By allowing for non zero vacuum expectation values for some of the fields that appear in the Hamiltonian constraint of canonical general relativity a time variable, with usual properties, can be identified; the constraint plays the role of…