Related papers: Constraining Curvature Parameters via Topology
Given the wealth of increasingly accurate cosmological observations, especially the recent results from the WMAP, and the development of methods and strategies in the search for cosmic topology, it is reasonable to expect that we should be…
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…
Observations of microwave background fluctuations can yield information not only about the geometry of the universe, but potentially about the topology of the universe. If the universe is negatively curved, then the characteristic scale for…
We use two model-independent methods to constrain the curvature of the universe. In the first method, we study the evolution of the curvature parameter ($\Omega_k^0$) with redshift by using the observations of the Hubble parameter and…
Geometry constrains but does not dictate the topology of the 3--dimensional space. In a locally spatially homogeneous and isotropic universe, however, the topology of its spatial section dictates its geometry. We show that, besides…
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…
The significance to which the cosmic microwave background observations by the satellite COBE can be used to refute a specific observationally based hypothesis for the global topology (3-manifold) of the Universe is investigated, by a new…
Recent observational results suggest that our universe is nearly flat and well modelled within a $\Lambda$CDM framework. The observed values of $\Omega_{m}$ and $\Omega_{\Lambda}$ inevitably involve uncertainties. Motivated by this, we make…
Cosmic microwave background (CMB) temperature and polarization observations indicate that in the best-fit $\Lambda$ Cold Dark Matter model of the Universe, the local geometry is consistent with at most a small amount of positive or negative…
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…
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…
A nontrivial topology of the spatial section of the universe is an observable, which can be probed for all locally homogeneous and isotropic universes, without any assumption on the cosmological density parameters. We discuss how one can…
Observational constraints guide one forcefully to examine models in which the matter density is substantially less than critical density. Particularly noteworthy are those which are consistent with inflation. For these models, microwave…
The cosmic microwave background radiation allows us to measure both the geometry and topology of the universe. It has been argued that the COBE-DMR data already rule out models that are multiply connected on scales smaller than the particle…
Multiply connected space sections of the universe on a scale smaller than the horizon size can leave an imprint on cosmic microwave background polarization maps, in such a way that the so-called ``circles-in-the-sky'' method can be used to…
The cosmic microwave background (CMB) is a unique probe of cosmological parameters and conditions. There is a connection between anisotropy in the CMB and the topology of the Universe. Adopting a universe with the topology of a 3-Torus, or…
Recently funded satellites will map the cosmic microwave background radiation with unprecedented sensitivities and angular resolutions. Assuming only primordial adiabatic scalar and tensor perturbations, we evaluate how accurately…
We study the effect of global topology of the spatial geometry on the cosmic microwave background (CMB) for closed flat and closed hyperbolic models in which the spatial hypersurface is multiply connected. If the CMB temperature…
The cosmographic approach is adopted to determine the spatial curvature (i.e., $\Omega_K$) combining the latest released cosmic chronometers data (CC), the Pantheon sample of type Ia supernovae observations, and the baryon acoustic…
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…