Cosmic microwave background anisotropies in multi-connected flat spaces
arXiv:astro-ph/0311314 · doi:10.1103/PhysRevD.69.103518
Abstract
This article investigates the signature of the seventeen multi-connected flat spaces in cosmic microwave background (CMB) maps. For each such space it recalls a fundamental domain and a set of generating matrices, and then goes on to find an orthonormal basis for the set of eigenmodes of the Laplace operator on that space. The basis eigenmodes are expressed as linear combinations of eigenmodes of the simply connected Euclidean space. A preceding work, which provides a general method for implementing multi-connected topologies in standard CMB codes, is then applied to simulate CMB maps and angular power spectra for each space. Unlike in the 3-torus, the results in most multi-connected flat spaces depend on the location of the observer. This effect is discussed in detail. In particular, it is shown that the correlated circles on a CMB map are generically not back-to-back, so that negative search of back-to-back circles in the WMAP data does not exclude a vast majority of flat or nearly flat topologies.
33 pages, 19 figures, 1 table. Submitted to PRD
References in corpus (26)
- First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
- A high resolution foreground cleaned CMB map from WMAP
- Cosmic Topology
- Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background
- Suppressing the lower Multipoles in the CMB Anisotropies
- Circles in the Sky: Finding Topology with the Microwave Background Radiation
- Is the Low CMB Quadrupole a Signature of Spatial Curvature?
- Cosmological constraints from Archeops
- The Cosmic Microwave Background Anisotropy Power Spectrum measured by Archeops
- Topology and the Cosmic Microwave Background
- Does the small CMB quadrupole moment suggest new physics?
- WMAP data and the curvature of space
- Topological Lensing in Spherical Spaces
- Eigenmodes of 3-dimensional spherical spaces and their application to cosmology
- Constraints on the topology of the universe from the 2-yr COBE data
- Detecting Topology in a Nearly Flat Spherical Universe
- Cosmic microwave background constraints on multi-connected spherical spaces
- New Restrictions on Spatial Topology of the Universe from Microwave Background Temperature Fluctuations
- How the Universe got its Spots
- COBE and Global Topology: An Example of the Application of the Identified Circles Principle
- A Counterexample to Claimed COBE Constraints on Compact Toroidal Universe Models
- Temperature Correlations in a Finite Universe
- COBE Constraints on a Compact Toroidal Low-density Universe
- How large is our universe?
- Geometric Gaussianity and Non-Gaussianity in the Cosmic Microwave Background
- The shape of a small universe: signatures in the cosmic microwave background
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- Planck 2013 results. XXVI. Background geometry and topology of the Universe
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- Vector theories in cosmology
- The optimal phase of the generalised Poincare dodecahedral space hypothesis implied by the spatial cross-correlation function of the WMAP sky maps
- A Hint of Poincaré Dodecahedral Topology in the WMAP First Year Sky Map
- Constraints on mode couplings and modulation of the CMB with WMAP data
- Planck 2015 results. XVIII. Background geometry & topology
- Do we Live in a "Small Universe"?
- Constraints on the Topology of the Universe: Extension to General Geometries
- Well-proportioned universes suppress CMB quadrupole
- The Status of Cosmic Topology after Planck Data
- Constraints on the topology of the Universe derived from the 7-year WMAP data
- Testing gaussianity, homogeneity and isotropy with the cosmic microwave background
- Footprints of Statistical Anisotropies
- Constraining topology in harmonic space
- An improved cosmic crystallography method to detect holonomies in flat spaces
- Cosmic microwave background multipole alignments in slab topologies
- Circles-in-the-sky searches and observable cosmic topology in a flat Universe
- Promise of Future Searches for Cosmic Topology
- The study of topology of the universe using multipole vectors
- Inflation, Large Branes, and the Shape of Space
- The residual gravity acceleration effect in the Poincare dodecahedral space
- Black Hole Final State Conspiracies
- The spectral action and cosmic topology
- Poincare dodecahedral space parameter estimates
- Topology beyond the horizon: how far can it be probed?
- Cosmic topology. Part I. Limits on orientable Euclidean manifolds from circle searches
- The coupling of topology and inflation in Noncommutative Cosmology
- Topological signatures in CMB temperature anisotropy maps
- On the detectability of non-trivial topologies
- Searching for planar signatures in WMAP
- Angular-planar CMB power spectrum
- Cosmic topology. Part IIa. Eigenmodes, correlation matrices, and detectability of orientable Euclidean manifolds
- Electromagnetic vacuum fluctuations and topologically induced motion of a charged particle
- Coupling of gravity to matter, spectral action and cosmic topology
- Cosmic microwave anisotropies in an inhomogeneous compact flat universe
- Stability of winding cosmic wall lattices with X type junctions
- Lagrange multiplier and Wess-Zumino variable as large extra dimensions in the torus universe
- What can the detection of a single pair of circles-in-the-sky tell us about the geometry and topology of the Universe ?
- The Hantzsche-Wendt Manifold in Cosmic Topology
- Vacuum Energy Density for Massless Scalar Fields in Flat Homogeneous Spacetime Manifolds with Nontrivial Topology
- Cosmic topology. Part IIIa. Microwave background parity violation without parity-violating microphysics
- A close examination of cosmic microwave background mirror-parity after Planck
- Probing spatial orientability of Friedmann--Robertson--Walker spatially flat spacetime
- Cosmic Topology : Twenty Years After
- Inquiring electromagnetic quantum fluctuations about the orientability of space
- Orbifold Line Topology and the Cosmic Microwave Background
- Cosmic topology. Part IVa. Classification of manifolds using machine learning: a case study with small toroidal universes
- Alternative route towards the change of metric signature
- Spinning Toroidal Brane Cosmology; A Classical and Quantum Survey
- A measure on the set of compact Friedmann-Lemaitre-Robertson-Walker models
- Searching for Stringy Topologies in the Cosmic Microwave Background
- Building Three-Dimensional Differentiable Manifolds Numerically
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- Scalar, Vector and Tensor Harmonics on the Flat Compact Orientable Three-Manifolds
- Betti Functionals as a Probe for Cosmic Topology
- Cosmic topology. Part IIIb. Eigenmodes and correlation matrices of spin-2 perturbations in orientable Euclidean manifolds
- Fractality in Cosmic Topology Models with Spectral Action Gravity