Related papers: Global hyperbolicity and factorization in cosmolog…
We present a detailed study of the cosmological evolution in general vector-tensor theories of gravity without potential terms. We consider the evolution of the vector field throughout the expansion history of the universe and carry out a…
A generic spacetime topology contains timelike boundaries. Making use of two such boundaries, we formulate a microscopic holographic dual that captures cosmological spacetime beyond the cosmic horizon patch, including the future wedge. We…
We consider the properties of an ensemble of universes as function of size, where size is defined in terms of the asymptotic value of the Hubble constant (or, equivalently, the value of the cosmological constant). We assume that standard…
We consider cosmological models in which a homogeneous isotropic universe is embedded as a 3+1 dimensional surface into a 4+1 dimensional manifold. The size of the extra dimension depends on time. It is small compared to the size of the…
Is the Universe (a spatial section thereof) finite or infinite? Knowing the global geometry of a Friedmann-Lema\^{\i}tre (FL) universe requires knowing both its curvature and its topology. A flat or hyperbolic (``open'') FL universe is {\em…
Quantum homogeneous vector bundles are introduced by a direct description of their sections in the context of Woronowicz type compact quantum groups. The bundles carry natural topologies inherited from the quantum groups, and their sections…
This review aims to cover the central aspects of current research in cosmic topology from a topological and observational perspective. Beginning with an overview of the basic concepts of cosmology, it is observed that though a determinant…
This article examines how the physical presence of field energy and particulate matter can be interpreted in terms of the topological properties of space-time. The theory is developed in terms of vector and matrix equations of exterior…
Dynamical aspects of cosmological model in an extended gravity theory have been investigated in the present work. We have adopted a simplified approach to obtain cosmic features, which in fact requires more involved calculations. A…
The role of global topology in the dynamics of the Universe is poorly understood. Along with observational programmes for determining the topology of the Universe, some small theoretical steps have recently been made. Heuristic…
In these lecture notes we will try to give an introduction to the use of the mathematics of fibre bundles in the understanding of some global aspects of gauge theories, such as monopoles and instantons. They are primarily aimed at beginning…
In this paper, we present a new cosmological model using fractal manifold. We prove that a space defined by this kind of manifold is an expanding space. This model provides us with consistent arguments pertaining to the relationship between…
General relativity does not allow one to specify the topology of space, leaving the possibility that space is multiply rather than simply connected. We review the main mathematical properties of multiply connected spaces, and the different…
The nature of space-time at high energy is an open question and the link between extra-dimensional theories with the physics of the Standard Model can not be established in a unique way. The compactification path is not unique and…
Starting from pure multidimensional gravity with curvature-nonlinear terms but no matter fields in the initial action, we obtain a cosmological model with two effective scalar fields related to the size of two extra factor spaces. The model…
In recent years, the intersection of algebra, geometry, and combinatorics with particle physics and cosmology has led to significant advances. Central to this progress is the twofold formulation of the study of particle interactions and…
The analogy between 1+3 splittings of the spacetime tangent bundle and the splitting of the tangent bundle to the bundle of linear frames into vertical and horizontal sub-bundles is described from the unifying standpoint of the geometry of…
The essence of the method of physics is inseparably connected with the problem of interplay between local and global properties of the universe. In the present paper we discuss this interplay as it is present in three major departments of…
We study the scalar curvature of spacelike hypersurfaces in the family of cosmological models known as generalized Robertson-Walker spacetimes, and give several rigidity results under appropriate mathematical and physical assumptions. On…
This paper reviews selected aspects of the growth of cosmological structure, covering the following general areas: (1) expected characteristics of linear density perturbations according to various candidate theories for the origin of…