Related papers: Cosmic topology. Part IIa. Eigenmodes, correlation…
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…
We study the eigenmodes of the spin-2 Laplacian in orientable Euclidean manifolds and their implications for the tensor-induced part of the cosmic microwave background (CMB) temperature and polarization anisotropies. We provide analytic…
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…
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…
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 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 standard cosmological model, which assumes statistical isotropy and parity invariance, predicts the absence of correlations between even-parity and odd-parity observables of the cosmic microwave background (CMB). Contrary to these…
Non-trivial spatial topology of the Universe may give rise to potentially measurable signatures in the cosmic microwave background. We explore different machine learning approaches to classify harmonic-space realizations of the microwave…
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…
This article investigates the computation of the eigenmodes of the Laplacian operator in multi-connected three-dimensional spherical spaces. General mathematical results and analytical solutions for lens and prism spaces are presented.…
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…
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…
In this work we investigate the standard deviation of the Cosmic Microwave Background (CMB) temperature gradient field as a signature for a multiply connected nature of the Universe. CMB simulations of a spatially infinite universe model…
The measurements of CMB anisotropy have opened up a window for probing the global topology of the universe on length scales comparable to and beyond the Hubble radius. For compact topologies, the two main effects on the CMB are: (1) the…
Recent observations seem to indicate that we live in a universe whose spatial sections are nearly or exactly flat. Motivated by this we study the problem of observational detection of the topology of universes with flat spatial sections. We…
If the assumption that physical space has a trivial topology is dropped, then the Universe may be described by a multiply connected Friedmann-Lema\^{\i}tre model on a sub-horizon scale. Specific candidates for the multiply connected space…
[Abridged] In a Universe with a detectable nontrivial spatial topology the last scattering surface contains pairs of matching circles with the same distribution of temperature fluctuations - the so-called circles-in-the-sky. Searches for…
We study the topology generated by the temperature fluctuations of the Cosmic Microwave Background (CMB) radiation, as quantified by the number of components and holes, formally given by the Betti numbers, in the growing excursion sets. We…
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…
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…