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Tarun Souradeep

Quantifying Statistical Isotropy Violation in the CMB. Tarun Souradeep. Indo-UK Seminar IUCAA, Pune (Aug. 10, 2011). I.U.C.A.A, Pune, India. CMB space missions. 1991-94. 2001-2010. 2009-2011. CMBPol/COrE 2020+. CMB Anisotropy & Polarization. CMB temperature T cmb = 2.725 K.

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Tarun Souradeep

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  1. Quantifying Statistical Isotropy Violation in the CMB Tarun Souradeep Indo-UK Seminar IUCAA, Pune (Aug. 10, 2011) I.U.C.A.A, Pune, India

  2. CMB space missions 1991-94 2001-2010 2009-2011 CMBPol/COrE 2020+

  3. CMB Anisotropy & Polarization CMB temperature Tcmb = 2.725 K -200  K <  T < 200  K  Trms~ 70 K • TpE~ 5  K • TpB ~ 10-100 nK • Temperature anisotropy T + two polarization modes E&B Four CMB spectra : ClTT, ClEE,ClBB,ClTE • Parity violation/sys. issues: ClTB,ClEB

  4. Cosmic “Super–IMAX” theater 0.5 Myr 14 GPc Here & Now (14 Gyr) Transparent universe Opaque universe

  5. Statistics of CMB CMB Anisotropy Sky map => Spherical Harmonic decomposition Gaussian CMB anisotropy completely specified by the angular power spectrum IF Statistical isotropy => Correlation function C(n,n’) is rotationally invariant

  6. Current Angular power spectrum 5th peak 3rd peak 6thpeak 4th peak Image Credit: NASA / WMAP Science Team

  7. Good old Cosmology, … New trend ! Total energy density Dark energy density Baryonic matter density ‘Standard’ cosmological model: Flat, CDM (with nearly Power Law primordial power spectrum) Talk: Dhiraj Hazra PPS with features NASA/WMAP science team

  8. Non-Parametric: Peak Location • (Amir Aghamousa, Mihir Arjunwadkar, TS arXiv:1107.0516) Talk: AmiR Aghamousa Day1

  9. Beyond Cl : • Detecting patterns in CMB • Universe on Ultra-Large scales: • Global topology • Global anisotropy/rotation • Breakdown of global syms, Magnetic field,… • Deflection fields • Observational artifacts: • Foreground residuals • Inhomogeneous noise, coverage • Non-circular beams (eg., Hanson et al. 2010)

  10. Statistics of CMB Possibilities: • Statistically Isotropic, Gaussian models • Statistically Isotropic, non-Gaussian models • Statistically An-isotropic, Gaussian models • Statistically An-isotropic, non-Gaussian models Ferreira & Magueijo 1997, Bunn & Scott 2000, Bond, Pogosyan & TS 1998, 2000

  11. Iso-contours of correlation around a point Radical breakdown of SI disjoint iso-contours multiple imaging Mild breakdown of SI Distorted iso-contours Statistically isotropic (SI) Circular iso-contours E.g.. Compact hyperbolic Universe . (Bond, Pogosyan & Souradeep 1998, 2002)

  12. SI violation, or ... Correlation patterns Can we measurecorrelation patterns? Beautiful Correlation patterns could underlie the CMB tapestry Figs. J. Levin the COSMIC CATCH is there is only one CMB sky !

  13. Measuring the SI correlation Statistical isotropy can be well estimated by averaging over the temperature product between all pixel pairs separated by an angle .

  14. Measuring the non-SI correlation In the absence of statistical isotropy Estimate of the correlation function from a sky map given by a single temperature product is poorly determined!! • (unless it is a KNOWN pattern) • Matched circles statistics (Cornish, Starkman, Spergel ‘98) • Anticorrelated ISW circle centers (Bond, Pogosyan,TS ‘98,’02) • Planar reflective symmetries (de OliveiraCosta, Smoot Starobinsky ’96)

  15. Bipolar Power spectrum (BiPS) :A Generic Measure of Statistical Anisotropy Bipolar multipole index A weighted average of the correlation function over all rotations Wigner rotation matrix Characteristic function

  16. Statistical Isotropy Correlation is invariant under rotations

  17. Bipolar Power spectrum (BiPS) :A Generic Measure of Statistical Anisotropy BiPoSH • Correlation is a two point function on a sphere • Inverse-transform Bipolar spherical harmonics. Clebsch-Gordan Linear combination of off-diagonal elements

  18. Recall: Coupling of angular momentum states BiPoSH coefficients : • Complete,Independent linear combinations of off-diagonal correlations. • Encompasses other specific measures of off-diagonal terms, such as • - Durrer et al. ’98 : • - Prunet et al. ’04 : BiPS:rotationally invariant

  19. Understanding BiPoSH coefficients

  20. Spherical harmonics Bipolar spherical harmonics Bipolar Power spectrum (BiPS) :A Generic Measure of Statistical Anisotropy

  21. Spherical harmonics Bipolar spherical harmonics Statistical Isotropyi.e., NO Patterns

  22. BIPOLAR maps of WMAP Hajian & Souradeep (PRD 2007) ILC-3 • Bipolar representation • Measure of statistical isotropy • Spectroscopy of Cosmic topology • Anisotropic power spectrum • Deflection fields (WL,…) • Diagnostic of systematic effects/observational artifacts in the map • Differentiate Cosmic vs. Galactic B-mode polarization ILC-1 Visualizing non-SI correlations Diff. • SI part corresponds to the “monopole” of the map.

  23. Preferred Directions in the universe Correlation function on a Torus (periodic box) SI violation at low wave-number, kR<1 More generally, (Hajian & Souradeep 2003) (Pullen & Kamionkowski 2008) Talk: Moumita Aich BipoSH for Torus

  24. Testing Statistical Isotropy of WMAP-3yr Hajian & Souradeep, (PRD 2007 ) Retain orientation information: Reduced BipoSH Outliers (> 95%) Filters

  25. BIPOLAR measurements by WMAP-7 team (Bennet et al. 2010) Non-zero Bipolar coeffs.!!! Sys. effect : beam distortion ? (Hanson et al. 2010) TALK by Santanu Das Image Credit: NASA / WMAP Science Team

  26. Revisting Statistics of BipoSH (Nidhi Joshi, AdityaRotti, TS, 2011) • ~Analytic PDF for BipoSH • Confirmed with MC simulations • Faster BipoSH code (20x) • Compute up to high multipoles Talk: Nidhi Joshi Day 2

  27. Even & odd Bipolar coefficients If only even L+l’+l contribute, it is becoming popular to use • Anisotropic P(k) • Linear order templates

  28. Even & odd parity BipoSH

  29. SI violation : Deflection field Gradient Curl WL:scalar WL: tensor/GW

  30. SI violation : Deflection field Brooks, Kamionkowski & Souradeep

  31. Deflection field: Even & Odd parity BipoSH Brooks, Kamionkowski & Souradeep 2011 WL: scalar WL: tensor

  32. BipoSH Measures of deflection field Estimators Variance

  33. CMB BipoSHs & Bispectra (Kamionkowski & Souradeep, PRD 2011) For deflection field BipoSH related to Bispectrum

  34. Odd parity Bispectra ? Flat sky intuition: has opposite sign in the two mirror configurations.

  35. Odd parity Bispectra For local NG model Flat sky approx In general

  36. Summary Thank you !!! • Current observations now allow a meaningful search for deviations from the `standard’ flat, CDM cosmology. • Anomalies in WMAP suggest possible breakdown down of statistical isotropy. • Bipolar harmonics provide a mathematically complete, well defined, representation of SI violation. • Possible to include SI violation in CMB arising both from direction dependent Primordial Power Spectrum, as well as, SI violation in the CMB photon distribution function. • BipoSHprovide a well structured representation of the systematic breakdown of rotational symmetry. • Bipolar observables have been measured in the WMAP data. • Systematic effects are important and must be quantified similar to signal • BipoSH coefficients can be separated into even and odd parity parts. • For a general deflection field, gradient & curl parts are represented by even & odd parity BipoSH, respectively. Eg., Weak lensing by scalar & tensor (or 2nd order scalar) perturbations. • Estimators for grad/curl deflections field harmonics in terms of even/odd BipoSH • BipoSH for correlated deflection field relate to Bispectra • Pointed to, hitherto unexplored, odd-parity bispectrum. • Minor modification to existing estimation methods for even-parity bispectra • Odd parity bispectrum may arise in exotic parity violations, but, also an interesting null test for usual bispectrum analysis.

  37. Statistical Isotropy: CMB Photon distribution (MoumitaAich & TS, PRD 2010) Statistical isotropy General: Non-Statistical isotropy

  38. Statistical Isotropy: CMB Photon distribution (MoumitaAich & TS, PRD 2010) Non-Statistical isotropic terms also free-stream to large multipole values

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