The study of topology of the universe using multipole vectors

Abstract

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 distribution on the sky for the lowest order multipoles together with the probability distribution function of statistics based on the sum of the dot products of the multipole vectors for both the simply-connected flat universe and universes with the topology of a 3-torus. The estimated probabilities of obtaining lower values for these statistics as compared to the 5-year WMAP data indicate that the observed alignment of the quadrupole and octopole is statistically favoured in a 3-torus topology where at least one dimension of the fundamental domain is significantly shorter than the diameter of the observable universe, as compared to the usual standard simply-connected universe. However, none of the obtained results are able to clearly rule out the latter (at more than 97% confidence level). Multipole vector statistics do not appear to be very sensitive to the signatures of a 3-torus topology if the shorter dimension of the domain becomes comparable to the diameter of the observable universe. Unfortunately, the signatures are also significantly diluted by the integrated Sachs-Wolfe effect.

16 pages, 17 figures, 2 tables, references added, updated to match version accepted by MNRAS

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Cited by in corpus (21)

• Planck 2013 results. XXIII. Isotropy and statistics of the CMB
• CMB Anomalies after Planck
• Is the Observable Universe Consistent with the Cosmological Principle?
• Searching for a Cosmological Preferred Axis: Union2 Data Analysis and Comparison with Other Probes
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• Planck 2015 results. XVIII. Background geometry & topology
• Anisotropy of Cosmic Acceleration
• The Status of Cosmic Topology after Planck Data
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• Bayesian analysis of anisotropic cosmologies: Bianchi VII_h and WMAP
• Large scale directional anomalies in the WMAP 5yr ILC map
• Topology beyond the horizon: how far can it be probed?
• Statistical Characterization of Temperature Patterns in Anisotropic Cosmologies
• CMB statistical isotropy confirmation at all scales using multipole vectors
• Cosmic Topology : Twenty Years After
• Cosmic topology. Part IVa. Classification of manifolds using machine learning: a case study with small toroidal universes
• Gravitational Interaction in the Chimney Lattice Universe
• Large Scale Cosmological Anomalies and Inhomogeneous Dark Energy
• Orbifold construction of the modes of the Poincare dodecahedral space
• Fréchet Vectors as sensitive tools for blind tests of CMB anomalies
• Gravitational potentials and forces in the Lattice Universe: a slab