Related papers: A Topological Signature in Cosmic Topology
If the universe has a nontrivial shape (topology) the sky may show multiple correlated images of cosmic objects. These correlations can be couched in terms of distance correlations. We propose a statistical quantity which can be used to…
A statistical quantity suitable for distinguishing simply-connected Robertson-Walker (RW) universes is introduced, and its explicit expressions for the three possible classes of simply-connected RW universes with an uniform distribution of…
Multi-connected universe models with space identification scales smaller than the size of the observable universe produce topological images of cosmic sources. We generalise to locally hyperbolic spaces the crystallographic method, aimed to…
We study the topological signature of euclidean isometries in pair separations histograms (PSH) and elucidate some unsettled issues regarding distance correlations between cosmic sources in cosmic crystallography. Reducing the noise of…
If the universe is multiply connected and small the sky shows multiple images of cosmic objects, correlated by the covering group of the 3-manifold used to model it. These correlations were originally thought to manifest as spikes in pair…
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:…
We study a multipole vector-based decomposition of cosmic microwave background (CMB) data in order to search for signatures of a multiconnected topology of the universe. Using 10^6 simulated maps, we analyse the multipole vector…
We revisit the classical and quantum cosmology of a universe in which a self interacting scalar field is coupled to gravity with a flat FRW type metric undergoing continuous signature transition. We arrange for quantum cosmologically…
In this paper, we present an algorithm that computes the topological signature for a given periodic motion sequence. Such signature consists of a vector obtained by persistent homology which captures the topological and geometric changes of…
Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…
We investigate which topological spaces can be constructed as topological realisations of higher-rank graphs. We describe equivalence relations on higher-rank graphs for which the quotient is again a higher-rank graph, and show that…
In this paper we find the most general self-similar, homogeneous and isotropic, Ricci flat cosmologies in 5D. These cosmologies show a number of interesting features: (i) the field equations allow a complete integration in terms of one…
We analyse a classical model of gravitation coupled to a self interacting scalar field. We show that, within the context of this model for Robertson-Walker cosmologies, there exist solutions in the spatially non-flat cases exhibiting…
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…
Universe models with compact spatial sections smaller than the observable universe produce a topological lens effect. Given a catalog of cosmic sources, we estimate the number of topological images in locally hyperbolic and locally elliptic…
The space-like hypersurface of the Universe at the present cosmological time is a three-dimensional manifold. A non-trivial global topology of this space-like hypersurface would imply that the apparently observable universe (the sphere of…
We study the topological components of the surface group representations into $\mathrm{SL}(2,\mathbb{R})$ and $\mathrm{PSL}(2,\mathbb{R})$. Utilizing the signature formula established in [14], we determine the number of connected components…
The early history of the universe might be described by a topological phase followed by a standard second phase of Einstein gravity. To study this scenario in its full generality, we consider a four-manifold of Euclidean signature in the…
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 present a method to construct signatures of periodic-like data. Based on topological considerations, our construction encodes information about the order and values of local extrema. Its main strength is robustness to reparametrisation…