Related papers: Cosmic Topology
The standard method for observationally confirming the existence of a predicted finite topology of the universe involves searching for the repetition of the same finite or extended source in different directions. However, serious problems…
General relativity marked the beginning of modern cosmology and it has since been at the centre of many of the key developments in this field. In the present review, we discuss the general-relativistic dynamics and perturbations of the…
What is the shape of the Universe? Is it curved or flat, finite or infinite ? Is space "wrapped around" to create ghost images of faraway cosmic sources? We review how tessellations allow to build multiply-connected 3D Riemannian spaces…
We show that most of cutoff measures of the multiverse violate some of the basic properties of probability theory when applied repeatedly to predict the results of local experiments. Starting from minimal assumptions, such as Markov…
I review some recent results on four-manifold invariants which have been obtained in the context of topological quantum field theory. I focus on three different aspects: (a) the computation of correlation functions, which give explicit…
Observational Cosmology has indeed made very rapid progress in recent years. The ability to quantify the universe has largely improved due to observational constraints coming from structure formation Measurements of CMB anisotropy and, more…
A holistic view of the cosmological appearance and development of space is obtained by studying space as a spherically closed surface of a 4-sphere in a zero energy balance between motion and gravitation. Such an approach re-establishes…
This article describes the theory of cosmological perturbations around a homogeneous and anisotropic universe of the Bianchi I type. Starting from a general parameterisation of the perturbed spacetime a la Bardeen, a complete set of gauge…
The common attribute of all Big Bang cosmologies is that they are based on the assumption that the universe is expanding. However examination of the evidence for this expansion clearly favours a static universe. The major topics considered…
We develop a new concept of non-positive curvature for metric spaces, based on intersection patterns of closed balls. In contrast to the synthetic approaches of Alexandrov and Buesemann, our concept also applies to metric spaces that might…
Homogeneity is a crucial, but poorly tested, assumption in cosmology. We introduce a new approach which allows us to place limits on the presence of localized structures within essentially our entire observable volume, using cosmic…
In light of the recent observational data coming from the sky we have two significant directions in the field of theoretical cosmology recently. First, we are now able to make use of present observations, such as the Planck and BICEP2 data,…
Over the last decades, observations with increasing quality have revolutionized our understanding of the general properties of the Universe. Questions posed for millenia by mankind about the origin, evolution and structure of the cosmos…
We note that in general there exist two basic aspects in any branch of physics, including cosmology - one dealing with the attributes of basic constituents and forces of nature, the other dealing with how structures arise from them and how…
The global shape (topology) of the Universe is not derivable from General Relativity but should be determined by observations. Here we propose a method for estimation of this shape using patterns of fundamental physical parameters, for…
Planck CMB temperature maps allow detection of large-scale departures from homogeneity and isotropy. We search for topology with a fundamental domain nearly intersecting the last scattering surface (comoving distance $\chi_r$). For most…
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…
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…
Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no…
Cosmology is undergoing an explosive period of activity, fueled both by new, accurate astrophysical data and by innovative theoretical developments. Cosmological parameters such as the total density of the Universe and the rate of…