Related papers: How Many Universes Do There Need To Be?
The global geometry of the universe is in principle as observable an attribute as local curvature. Previous studies have established that if the universe is wrapped into a flat hypertorus, the simplest compact space, then the fundamental…
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…
We define a universe as the contents of a spacetime box with comoving walls, large enough to contain essentially all phenomena that can be conceivably measured. The initial time is taken as the epoch when the lowest CMB modes undergo…
Is the universe finite or infinite, and what shape does it have? These fundamental questions, of which relatively little is known, are typically studied within the context of the standard model of cosmology where the universe is assumed to…
Many cosmological models assume or imply that the total size of the universe is very large, perhaps even infinite. Here we argue instead that the universe might be comparatively small, in fact not much larger than the currently observed…
We study here what it means for the Universe to be nearly flat, as opposed to exactly flat. We give three definitions of nearly flat, based on density, geometry and dynamics; all three definitions are equivalent and depend on a single…
Conventional thinking says the universe is infinite. But it could be finite and relatively small, merely giving the illusion of a greater one, like a hall of mirrors. Recent astronomical measurements add support to a finite space with a…
If the universe is infinite now it has always been infinite. This is the opinion of many astronomers today as can be concluded from the following series of interviews, but the opinions differ much more than I had expected. Many astronomers…
The question of determining the spatial geometry of the Universe is of greater relevance than ever, as precision cosmology promises to verify inflationary predictions about the curvature of the Universe. We revisit the question of what can…
How much matter is there in the universe? Does the universe have the critical density needed to stop its expansion, or is the universe underweight and destined to expand forever? We show that several independent measures, especially those…
Scientists have measured that what we can see of space is about a billion billion billion billion billion billion billion billion billion (10^81) times the volume of an average human. Inflationary theory suggests that the entirety of space…
Suppose we have identified three clusters of galaxies as being topological copies of the same object. How does this information constrain the possible models for the shape of our Universe? It is shown here that, if the Universe has flat…
The Universe is a physical object. Physical objects have shapes and sizes. General relativity is insufficient to describe the global shape and size of the Universe: the Hilbert-Einstein equations only treat limiting quantities towards an…
In this paper we work out a multiverse scenario whose physical characteristics enable us to advance the following the conjecture that whereas the physics of particles and fields is confined to live in the realm of the whole multiverse…
Questions such as whether we live in a spatially finite universe, and what its shape and size may be, are among the fundamental open problems that high precision modern cosmology needs to resolve. These questions go beyond the scope of…
The Cosmological Principle states that the universe is both homogeneous and isotropic. This, alone, is not enough to specify the global geometry of the spacetime. If we were able to measure both the Hubble constant and the energy density we…
If the topology of the universe is compact we show how it significantly changes our assessment of the naturalness of the observed structure of the universe and the likelihood of its present state of high isotropy and near flatness arising…
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…
Modern observations based on general relativity indicate that the spatial geometry of the expanding, large-scale Universe is very nearly Euclidean. This basic empirical fact is at the core of the so-called "flatness problem", which is…
The Universe could be spatially flat, positively curved or negatively curved. Each option has been popular at various times, partly affected by an understanding that models tend to evolve away from flatness. The curvature of the Universe is…