相关论文: Constraining topology in harmonic space
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…
The limit of energies of a sequence of harmonic maps as their annular domains approach the boundary of moduli space depends upon the boundary point approached. The infinite energy case is associated with limits of images containing ruled…
While the standard, six-parameter, spatially flat $\Lambda$CDM model has been highly successful, certain anomalies in the cosmic microwave background bring out a tension between this model and observations. The statistical significance of…
Harmonic analysis is a tool to infer cosmic topology from the measured astrophysical cosmic microwave background CMB radiation. For overall positive curvature, Platonic spherical manifolds are candidates for this analysis. We combine the…
Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…
We present a new data analysis method to study rectangular T^3 ``small universes" with one or two of its dimensions significantly smaller than the present horizon (which we refer to as T^1- and T^2-models, respectively). We find that the 4…
We calculate the CMB anisotropy in compact hyperbolic universe models using the regularized method of images described in paper-I, including the 'line-of-sight `integrated Sachs-Wolfe' effect, as well as the last-scattering surface terms.…
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…
We compute the covariance expected between the spherical harmonic coefficients $a_{\ell m}$ of the cosmic microwave temperature anisotropy if the universe had a compact topology. For fundamental cell size smaller than the distance to the…
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…
According to the separate universe conjecture, spherically symmetric sub-regions in an isotropic universe behave like mini-universes with their own cosmological parameters. This is an excellent approximation in both Newtonian and general…
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…
Cosmological parameters are constrained by a wide variety of observations. We examine the concordance diagram for modern measurements of the Hubble constant, the shape parameter from large scale structure, the cluster baryon fraction, and…
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…
We assess the accuracy with which Omega and Lambda can be measured by combining various types of upcoming experiments. Useful expressions for the Fisher information matrix are derived for classical cosmological tests involving luminosity…
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…
The Harmonic Mapping Problem asks when there exists a harmonic homeomorphism between two given domains. It arises in the theory of minimal surfaces and in calculus of variations, specifically in hyperelasticity theory. We investigate this…
The question of the global topology of the Universe (cosmic topology) is still open. In the $\Lambda$CDM concordance model it is assumed that the space of the Universe possesses the trivial topology of $\mathbb{R}^3$ and thus that the…
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…
Given a finite collection of probability measures defined on subsets of a measurable space, how can we determine if they are compatible, in the sense that they can be realized as conditional distributions of a single probability measure on…