Related papers: Constraining topology in harmonic space
Gaussianity of the cosmological perturbations in the universe is one of the key predictions of standard inflation, but it is violated by other models of structure formation such as topological defects. We present the first test of the…
We consider problems of estimation of structured covariance matrices, and in particular of matrices with a Toeplitz structure. We follow a geometric viewpoint that is based on some suitable notion of distance. To this end, we overview and…
We introduce a method of quantum tomography for a continuous variable system in position and momentum space. We consider a single two-level probe interacting with a quantum harmonic oscillator by means of a class of Hamiltonians, linear in…
The next generation of cosmological surveys will operate over unprecedented scales, and will therefore provide exciting new opportunities for testing general relativity. The standard method for modelling the structures that these surveys…
We consider the space of complete and separable metric spaces which are equipped with a probability measure. A notion of convergence is given based on the philosophy that a sequence of metric measure spaces converges if and only if all…
The current cosmological dark sector (dark matter plus dark energy) is challenging our comprehension about the physical processes taking place in the Universe. Recently, some authors tried to falsify the basic underlying assumptions of such…
In this paper we examine the use of topological methods for multivariate statistics. Using persistent homology from computational algebraic topology, a random sample is used to construct estimators of persistent homology. This estimation…
In the mini-superspace approximation to cosmology, the canonical measure can be used to compute probabilities when a cutoff is introduced in the phase space to regularize the divergent measure. However, the region initially constrained by a…
Current and upcoming surveys will measure the cosmological parameters with an extremely high accuracy. The primary goal of these observations is to eliminate some of the currently viable cosmological models created to explain the late time…
We study harmonic map sequences from surfaces to compact homogeneous spaces. For sequences developing a single bubble, we derive refined asymptotic expansions in the neck region and prove new obstruction relations among the leading…
In this paper, we explore how to use topological tools to compare dimension reduction methods. We first make a brief overview of some of the methods often used dimension reduction such as Isometric Feature Mapping, Laplacian Eigenmaps, Fast…
The shortest distance around the Universe through us is unlikely to be much larger than the horizon diameter if microwave background anomalies are due to cosmic topology. We show that observational constraints from the lack of matched…
We review observational tests for the homogeneity of the Universe on large scales. Redshift and peculiar velocity surveys, radio sources, the X-Ray Background, the Lyman-$\alpha$ forest and the Cosmic Microwave Background are used to set…
A self-consistent modular cosmology scenario and its testability in view of future CMB experiments are discussed. Particular attention is drawn to the enhanced symmetric points in moduli space which play crucial roles in our scenario. The…
Large scale density modes are difficult to measure because they are sensitive to systematic observational errors in galaxy surveys, but we can study them indirectly by observing their impact on small scale perturbations. Cosmological…
The space of inflationary models is vast, containing wide varieties of mechanisms, symmetries, and spectra of particles. Consequently, the space of observational signatures is similarly complex. Hence, it is natural to look for boundaries…
Spatial aspects of computation are becoming increasingly relevant in Computer Science, especially in the field of collective adaptive systems and when dealing with systems distributed in physical space. Traditional formal verification…
This paper develops new tools for understanding surfaces with more than one end (and usually, of infinite topology) which properly minimally embed into Euclidean three-space. On such a surface, the set of ends forms a compact Hausdorff…
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…
We study the effect of the topology of universe by gauging the non-relativistic particle model on the torus and 3-torus, using the symplectic formalism of constrained systems and embedding those models on extended phase-spaces. Also, we…