Related papers: Betti Functionals as a Probe for Cosmic Topology
The topology and geometry of random fields - in terms of the Euler characteristic and the Minkowski functionals - has received a lot of attention in the context of the Cosmic Microwave Background (CMB), as the detection of primordial…
The standard cosmological model does not determine the spatial topology of the universe. This article revisits the signature of a non-trivial topology on the properties of the cosmic microwave background anisotropies. We show that the…
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…
We reexamine the possibility of the detection of the cosmic topology in nearly flat hyperbolic Friedmann-Lemaitre-Robertson-Walker (FLRW) universes by using patterns repetition. We update and extend our recent results in two important ways:…
The temperature and polarization of the cosmic microwave background (CMB), as measured today, may offer key insights into the topology of the early universe prior to inflation, for example, by discriminating between flat and warped…
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…
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…
We study the topology of the Megaparsec Cosmic Web in terms of the scale-dependent Betti numbers, which formalize the topological information content of the cosmic mass distribution. While the Betti numbers do not fully quantify topology,…
Spatial correlations of the cubic 3-torus topology are analysed using the Planck 2013 data. The spatial-correlation method for detecting multiply connected spaces is based on the fact that positions on the cosmic microwave background (CMB)…
We impose constraints on the topology of the Universe determined from a search for matched circles in the cosmic microwave background (CMB) temperature anisotropy patterns of the 7-year WMAP data. We pay special attention to the sensitivity…
If the Universe has non-trivial spatial topology, observables depend on both the parameters of the spatial manifold and the position and orientation of the observer. In infinite Euclidean space, most cosmological observables arise from the…
Recent studies of the detectability of cosmic topology of nearly flat universes have often concentrated on the range of values of $\Omega_{0}$ given by current observations. Here we study the consequences of taking the bounds on…
We study the effect of a finite topology on the temperature correlations of the cosmic microwave background in a flat universe. Analytic expressions for the angular power spectrum are given for all possible finite flat models. We examine…
If the Universe has non-trivial spatial topology, observables depend on both the parameters of the spatial manifold and the position and orientation of the observer. In infinite Euclidean space, most cosmological observables arise from the…
The global topology of the Universe could, in principle, affect quantum systems through boundary condition constraints. We investigate this connection by analyzing how compact, flat, cosmologically inspired topologies, specifically the…
Although the cubic T^3 "small universe" has been ruled out by COBE/DMR results as an interesting cosmological model, we still have the possibility of living in a universe with a more anisotropic topology such as a rectangular T^3 "small…
The Einstein field equations of general relativity constrain the local curvature at every point in spacetime, but say nothing about the global topology of the Universe. Cosmic microwave background anisotropies have proven to be the most…
An important, and potentially detectable, signature of a non-trivial topology for the universe is the presence of so called circles-in-the-sky in the cosmic microwave background (CMB). Recent searches, confined to antipodal and nearly…
CMB anisotropy measurements have brought the issue of global topology of the universe from the realm of theoretical possibility to within the grasp of observations. The global topology of the universe modifies the correlation properties of…
Non-trivial spatial topology of the Universe can imprint potentially observable signatures on the cosmic microwave background (CMB). In this study, we investigate how deviations from the standard nearly-scale-free primordial power spectrum…