Cosmic topology. Part I. Limits on orientable Euclidean manifolds from circle searches

Abstract

The Einstein field equations of general relativity constrain the local curvature at every point in spacetime, but say nothing about the global topology of the Universe. Cosmic microwave background anisotropies have proven to be the most powerful probe of non-trivial topology since, within $\Lambda$CDM, these anisotropies have well-characterized statistical properties, the signal is principally from a thin spherical shell centered on the observer (the last scattering surface), and space-based observations nearly cover the full sky. The most generic signature of cosmic topology in the microwave background is pairs of circles with matching temperature and polarization patterns. No such circle pairs have been seen above noise in the WMAP or Planck temperature data, implying that the shortest non-contractible loop around the Universe through our location is longer than 98.5% of the comoving diameter of the last scattering surface. We translate this generic constraint into limits on the parameters that characterize manifolds with each of the nine possible non-trivial orientable Euclidean topologies, and provide a code which computes these constraints. In all but the simplest cases, the shortest non-contractible loop in the space can avoid us, and be shorter than the diameter of the last scattering surface by a factor ranging from 2 to at least 6. This result implies that a broader range of manifolds is observationally allowed than widely appreciated. Probing these manifolds will require more subtle statistical signatures than matched circles, such as off-diagonal correlations of harmonic coefficients.

arXiv comment22 pages, 7 figures. v3: Corrected Figs. 3, 4, and 5 as published in Erratum. v4: Corrected omission of late-contributing author to author list

References in corpus (25)

• The significance of the largest scale CMB fluctuations in WMAP
• Planck 2013 results. XXIII. Isotropy and statistics of the CMB
• Planck 2018 results. VII. Isotropy and Statistics of the CMB
• Cosmic Topology
• Planck 2015 results. XVI. Isotropy and statistics of the CMB
• CMB Anomalies after Planck
• Circles in the Sky: Finding Topology with the Microwave Background Radiation
• Planck 2013 results. XXVII. Doppler boosting of the CMB: Eppur si muove
• Constraining the Topology of the Universe
• Planck 2015 results. XVIII. Background geometry & topology
• Cosmic microwave background anisotropies in multi-connected flat spaces
• Extending the WMAP Bound on the Size of the Universe
• Can COBE see the shape of the universe?
• On Determining the Topology of the Observable Universe via 3-D Quasar Positions
• Constraints on the Topology of the Universe: Extension to General Geometries
• Constraints on the topology of the Universe derived from the 7-year WMAP data
• Measuring the Topology of the Universe
• An improved cosmic crystallography method to detect holonomies in flat spaces
• Circles-in-the-sky searches and observable cosmic topology in a flat Universe
• A search for cosmic topology in the final WMAP data
• Constraining the topology of the Universe using the polarised CMB maps
• Ghosts of the Milky Way: a search for topology in new quasar catalogues
• Cosmic Crystallography
• A search for nontoroidal topological lensing in the Sloan Digital Sky Survey quasar catalog
• Circles in the Sky: Finding Topology with the Microwave Background Radiation

Cited by in corpus (10)

• $\Lambda$CDM Tensions: Localising Missing Physics through Consistency Checks
• Promise of Future Searches for Cosmic Topology
• Cosmic topology. Part IIa. Eigenmodes, correlation matrices, and detectability of orientable Euclidean manifolds
• A small Universe
• Cosmic topology. Part IIIa. Microwave background parity violation without parity-violating microphysics
• Cosmic topology. Part IVa. Classification of manifolds using machine learning: a case study with small toroidal universes
• Cosmic topology. Part Ic. Limits on lens spaces from circle searches
• Betti Functionals as a Probe for Cosmic Topology
• Cosmic topology. Part IIIb. Eigenmodes and correlation matrices of spin-2 perturbations in orientable Euclidean manifolds
• Bianchi cosmologies in a Thurston-based theory of gravity