Computing CMB Anisotropy in Compact Hyperbolic Spaces

Abstract

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 breaking of statistical isotropy in characteristic patterns determined by the photon geodesic structure of the manifold and (2) an infrared cutoff in the power spectrum of perturbations imposed by the finite spatial extent. We present a completely general scheme using the regularized method of images for calculating CMB anisotropy in models with nontrivial topology, and apply it to the computationally challenging compact hyperbolic topologies. This new technique eliminates the need for the difficult task of spatial eigenmode decomposition on these spaces. We estimate a Bayesian probability for a selection of models by confronting the theoretical pixel-pixel temperature correlation function with the COBE-DMR data. Our results demonstrate that strong constraints on compactness arise: if the universe is small compared to the `horizon' size, correlations appear in the maps that are irreconcilable with the observations. If the universe is of comparable size, the likelihood function is very dependent upon orientation of the manifold wrt the sky. While most orientations may be strongly ruled out, it sometimes happens that for a specific orientation the predicted correlation patterns are preferred over the conventional infinite models.

15 pages, LaTeX (IOP style included), 3 color figures (GIF) in separate files. Minor revision to match the version accepted in Class. Quantum Grav.: Proc. of Topology and Cosmology, Cleveland, 1997. The paper can be also downloaded from http://www.cita.utoronto.ca/~pogosyan/cwru_proc.ps.gz

References in corpus (3)

• Circles in the Sky: Finding Topology with the Microwave Background Radiation
• Flat Spots: topological signatures of an open universe in COBE sky maps
• The topology of the universe: the biggest manifold of them all

Cited by in corpus (34)

• Radical Compression of Cosmic Microwave Background Data
• Circles in the Sky: Finding Topology with the Microwave Background Radiation
• Measuring Statistical isotropy of the CMB anisotropy
• Topology and the Cosmic Microwave Background
• Planck 2013 results. XXVI. Background geometry and topology of the Universe
• Statistical Isotropy of the Wilkinson Microwave Anisotropy Probe Data: A Bipolar Power Spectrum Analysis
• Planck 2015 results. XVIII. Background geometry & topology
• CMB Anisotropy of the Poincare Dodecahedron
• Eigenmodes of 3-dimensional spherical spaces and their application to cosmology
• Simulating Cosmic Microwave Background maps in multi-connected spaces
• Constraints on the Topology of the Universe: Extension to General Geometries
• Hyperbolic Universes with a Horned Topology and the CMB Anisotropy
• CMB Anisotropy in Compact Hyperbolic Universes I: Computing Correlation Functions
• CMB Anisotropy in Compact Hyperbolic Universes II: COBE Maps and Limits
• The Cosmic Microwave Background for a Nearly Flat Compact Hyperbolic Universe
• Constraining Large Scale Structure Theories with the Cosmic Background Radiation
• Nonperturbative effects in the Standard Model with gauged 1-form symmetry
• Measuring Statistical Isotropy of CMB Anisotropy
• The Fluctuations of the Cosmic Microwave Background for a Compact Hyperbolic Universe
• A small universe after all?
• Statistical isotropy of the Cosmic Microwave Background
• Temperature correlations in a compact hyperbolic universe
• COBE Constraints on a Compact Toroidal Low-density Universe
• Perturbations on steady spherical accretion in Schwarzschild geometry
• Topological signatures in CMB temperature anisotropy maps
• Three-dimensional Topology-Independent Methods to Look for Global Topology
• Topology of the universe from COBE-DMR; a wavelet approach
• What have we already learned from the CMB?
• The Hantzsche-Wendt Manifold in Cosmic Topology
• Bayesian inference on the sphere beyond statistical isotropy
• SIToolBox : A package for Bayesian estimation of the isotropy violation in the CMB sky
• Probing beyond the Cosmic Horizon
• `Standard' Cosmological model & beyond with CMB
• Cosmological quests in the CMB sky