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CMB and the Topology of the Universe

CMB and the Topology of the Universe. Dmitri Pogosyan, UAlberta. With: Tarun Souradeep Dick Bond and: Carlo Contaldi Adam Hincks. Simon White, Garching, last week: Open questions in Cosmology: Is our Universe is finite or infinite? Is its space curved ? ….

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CMB and the Topology of the Universe

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  1. CMB and the Topology of the Universe Dmitri Pogosyan, UAlberta With: Tarun Souradeep Dick Bond and: Carlo Contaldi Adam Hincks Simon White, Garching, last week: Open questions in Cosmology: Is our Universe is finite or infinite? Is its space curved ? …. COSMO-05, Bonn 2005

  2. Preferred parameter region, tot=1.02 ± 0.02 Ωtot=1.01 RLSS/Rcurv=0.3 COSMO-05, Bonn 2005

  3. How Big is the Observable Universe ? Relative to the local curvature & topological scales COSMO-05, Bonn 2005

  4. Dirichlet domain and dimensions of the compact space RLS < R< COSMO-05, Bonn 2005

  5. Dirichlet domain and dimensions of the compact space RLS > R> COSMO-05, Bonn 2005

  6. Absence of large scale power COSMO-05, Bonn 2005 NASA/WMAP science team

  7. Correlation function of isotropic CMB Oscillations in the angular spectrum come from this break COSMO-05, Bonn 2005

  8. Perturbations in Compact space • Spectrum has the lowest eigenvalue. • Spectrum is discrete, hence statistics in general is anisotropic, especially at large scales. • Statistical properties can be inhomogeneous. • However, perturbations are Gaussian, and CMB temperature fluctuations are fully described by pixel-pixel correlation matrix CT(p,p’) • We implemented general method of images to compute CT(p,p’) for arbitrary compact topology (Bond,Pogosyan, Souradeep, 1998,2002) COSMO-05, Bonn 2005

  9. Pixel-pixel correlation with compact topology (using method of images, BPS, Phys Rev D. 2000) COSMO-05, Bonn 2005

  10. Example of strong correlation on last scattering surface These two points on LSS are identical And so are these COSMO-05, Bonn 2005

  11. Correlated Circles(after Cornish, Spergel, Starkman et al, 1998,2004) (Figure: Bond, Pogosyan & Souradeep 1998, 2002) COSMO-05, Bonn 2005

  12. Temperature along the correlated circles(pure LSS signal) COSMO-05, Bonn 2005

  13. Temperature along the correlated circles (ISW modification) COSMO-05, Bonn 2005

  14. COSMO-05, Bonn 2005

  15. Positive curvature multiconnected universe ? : Perhaps, a Poincare dodecahedron “Soccer ball cosmos” ? COSMO-05, Bonn 2005

  16. Isotropic Cpp’ D/RLSS=10 COSMO-05, Bonn 2005

  17. Surface term to DT/T D/RLSS=0.3 COSMO-05, Bonn 2005

  18. Complete, surface and integrated large-angle ΔT/T D/RLSS=0.3 COSMO-05, Bonn 2005

  19. Variation of the pixel variance D/RLSS=0.3 COSMO-05, Bonn 2005

  20. Constraining the models from maps • Complete topological information is retained when comparison with data is done on map level • Low res (Nside=16) maps contain most information, although special techniques as circle searching may benefit from finer pixalization. The cost – additional small scale effects which mask topological correlations. • Main signal comes from effects, localized in space, e.q on LSS. But even integrated along the line of sight contributions retain signature of compact topology. • Orientation of the space (and, possibly, position of observer) are additional parameters to consider. What is the prior for them ? COSMO-05, Bonn 2005

  21. Likelehood comparison ofcompact closed versus flat Universe with =0.7 COSMO-05, Bonn 2005

  22. WMAP: Angular power spectrum NASA/WMAP science team COSMO-05, Bonn 2005

  23. Single index n: (l,m) -> n Diagonal COSMO-05, Bonn 2005

  24. Inadequacy of isotropized Cl’s: alm cross correlation Very small space Just a bit smaller than LSS 2 3 4 5 6 7 8 9 10 2 3 4 5 6 7 8 9 10 COSMO-05, Bonn 2005

  25. Compression to isotropic Cls is lossy Inhanced cosmic variance of Cl’s COSMO-05, Bonn 2005

  26. Bipolar Power spectrum (BiPS) :A Generic Measure of Statistical Anisotropy Bipolar multipole index A weighted average of the correlation function over all rotations Except for when (This slide is provided as a free advertisement for T. Souradeep talk, Wednesday) COSMO-05, Bonn 2005

  27. Conclusions • A fundamental question – whether our Universe is finite or infinite –is still open. • The region near Otot=1 is rich with possibilities, with negatively or positively curved or flat spaces giving rise to distinct topological choices. • Modern CMB data shows that small Universes with V < VLS are failing to describe the temperature maps. Reason – complex correlation are not really observed (in line with circle finding results). • This is despite the fact that it is not too difficult to fit the low l suppression of isotropized angular power spectrum. • Integrated along the line of sight contribution to temperature anisotropy masks and modifies topology signature. It must be taken into account for any accurate quantitative restrictions on compact spaces. • Full likelihood analysis assumes knowledge of the models. Model independent search for statistical anisotropy calls for specialized techniques – see talk on BiPS by Tarun Souradeep on Wednesday. COSMO-05, Bonn 2005

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