Related papers: Constraining topology in harmonic space
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…
We study the possibility that the universe has compact topologies T^3, T^2 x R^1, or S^1 x R^2 using the seven-year WMAP data. The maximum likelihood 95% confidence intervals for the size L of the compact direction are 1.7 < L/L_0 < 2.1,…
The standard method for observationally confirming the existence of a predicted finite topology of the universe involves searching for the repetition of the same finite or extended source in different directions. However, serious problems…
The first year data from the Wilkinson Microwave Anisotropy Probe are used to place stringent constraints on the topology of the Universe. We search for pairs of circles on the sky with similar temperature patterns along each circle. We…
A search for matched circle pairs of similar temperature fluctuations in the final WMAP 9yr data is carried out. Such a signature is expected if the space of the Universe is multiply connected. We investigate the relation between the pixel…
Great efforts are currently being channeled into ground- and balloon-based CMB experiments, mainly to explore anisotropy on small angular scales and polarization. To optimize instrumental design and assess experimental prospects, it is…
The Cosmic Microwave Background (CMB) power spectrum derived from the first year WMAP data demonstrates an intriguing lack of power at large scales that cannot be accounted for within the framework of the standard cosmological model. We…
Homogeneity is a crucial, but poorly tested, assumption in cosmology. We introduce a new approach which allows us to place limits on the presence of localized structures within essentially our entire observable volume, using cosmic…
Tensions between cosmological measurements by different surveys or probes have always been important --- and are presently much discussed --- as they may lead to evidence of new physics. Several tests have been devised to probe the…
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…
We study two different methods to test Gaussianity in CMB maps. One of them is based on the partition function and the other on the morphology of hot and cold spots. The partition function contains information on all the moments and scales,…
In a variety of applications it is important to extract information from a probability measure $\mu$ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and possibly conditioned) continuous time…
A non-trivial spatial topology of the Universe is a potentially observable attribute, which can be probed through the circles-in-the-sky for all locally homogeneous and isotropic universes with no assumptions on the cosmological parameters.…
Although the broad outlines of the appropriate pipeline for cosmological likelihood analysis with CMB data has been known for several years, only recently have we had to contend with the full, large-scale, computationally challenging…
We compute the effects of a compact flat universe on the angular correlation function, the angular power spectrum, the circles-in-the-sky signature, and the covariance matrix of the spherical harmonics coefficients of the cosmic microwave…
Assessing the consistency of parameter constraints derived from different cosmological probes is an important way to test the validity of the underlying cosmological model. In an earlier work [Nicola et al., 2017], we computed constraints…
By utilizing large-scale graph analytic tools implemented in the modern Big Data platform, Apache Spark, we investigate the topological structure of gravitational clustering in five different universes produced by cosmological $N$-body…
We investigate harmonic maps from weighted graphs into metric spaces that locally admit unique centers of gravity, like Alexandrov spaces with upper curvature bounds. We prove an existence result by constructing an iterative geometric…
This paper summarizes the physical mechanisms that encode the type and quantity of cosmological matter in the properties of large-scale structure, and reviews the application of such tests to current datasets. The key lengths of the horizon…
Detecting spatial patterns is fundamental to scientific discovery, yet current methods lack statistical consensus and face computational barriers when applied to large-scale spatial omics datasets. We unify major approaches through a single…