Related papers: Constraining topology in harmonic space
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…
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…
With the high-precision data from current and upcoming experiments, it becomes increasingly important to perform consistency tests of the standard cosmological model. In this work, we focus on consistency measures between different data…
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…
Discordance in the $\Lambda$CDM cosmological model can be seen by comparing parameters constrained by CMB measurements to those inferred by probes of large scale structure. Recent improvements in observations, including final data releases…
WMAP observations have accurately determined the position of the first two peaks and dips in the CMB temperature power spectrum. These encode information on the ratio of the distance to the last scattering surface to the sound horizon at…
Do current observational data confirm the assumptions of the cosmological principle, or is there statistical evidence for deviations from spatial homogeneity on large scales? To address these questions, we developed a flexible framework…
Planck CMB temperature maps allow detection of large-scale departures from homogeneity and isotropy. We search for topology with a fundamental domain nearly intersecting the last scattering surface (comoving distance $\chi_r$). For most…
The latent space model is one of the well-known methods for statistical inference of network data. While the model has been much studied for a single network, it has not attracted much attention to analyze collectively when multiple…
To date, no compelling evidence has been found that the universe has non-trivial spatial topology. Meanwhile, anomalies in the observed CMB temperature map, such as the lack of correlations at large angular separations, remain…
What is the shape of space is a long-standing question in cosmology. In this talk I review recent advances in cosmic topology since it has entered a new era of experimental tests. High redshift surveys of astronomical sources and accurate…
The cosmic microwave background radiation allows us to measure both the geometry and topology of the universe. It has been argued that the COBE-DMR data already rule out models that are multiply connected on scales smaller than the particle…
``One could imagine that as a result of enormously extended astronomical experience, the entire universe consists of countless identical copies of our Milky Way, that the infinite space can be partitioned into cubes each containing an…
We explore the topology of configuration spaces of hard disks experimentally, and show that several changes in the topology can already be observed with a small number of particles. The results illustrate a theorem of Baryshnikov, Bubenik,…
The (large angle) COBE DMR data can be used to probe the global topology of our universe on scales comparable to and just beyond the present ``horizon''. For compact topologies, the two main effects on the CMB are: [1] the breaking of…
We construct nonsingular cyclic cosmologies that respect the null energy condition, have a large hierarchy between the minimum and maximum size of the universe, and are stable under linearized fluctuations. The models are supported by a…
I explain the difficulty of making various concepts of and relating to probability precise, rigorous and physically significant when attempting to apply them in reasoning about objects (e.g., spacetimes) living in infinite-dimensional…
Current astrophysical models of the interstellar medium assume that small scale variation and noise can be modelled as Gaussian random fields or simple transformations thereof, such as lognormal. We use topological methods to investigate…
The topology of the large-scale structure of the universe contains valuable information on the underlying cosmological parameters. While persistent homology can extract this topological information, the optimal method for parameter…
Inflation predicts that quantum fluctuations determine the large scale structure of the Universe. This raises the striking possibility that quantum mechanics, developed to describe nature at short distances, can be tested by studying nature…