Challenging                    the             Isotropic CosmosCTACC Colloquium     Tarun Souradeep  AIMS, Cape Town     I...
CMB space missions1991-94          2001-2010                      2009-2011                           CMBPol/COrE         ...
Cosmic Microwave BackgroundPristine relic of ahot, dense & smoothearly universe -Hot Big Bang modelPost-recombination :Fre...
Cosmic   “Super–IMAX”       theater                            0.5 Myr              Here              & Now             (1...
CMB Anisotropy & Polarization                                        CMB temperature                                      ...
Statistics of CMBCMB Anisotropy Sky map => Spherical Harmonic decomposition                                             ∞ ...
Fig. M. White 1997   The Angular power spectrum of        CMB anisotropy depends                                C     sens...
Dissected CMB Angular power spectrum •Low multipole :     • Moderate  multipole :    • High multipole :Sachs-Wolfe plateau...
Cosmic Acoustics: Ping the ‘Cosmic drum’                                         150 Mpc                              More...
WMAP: Angular power spectrumIndependent, self contained analysis of WMAP multi-frequency maps           Saha, Jain, Sourad...
Peaks of the angular power spectrum                               (74.1±0.3, 219.8±0.8)                               (74....
Peak heights and ratios   Cosmological Parametersωb ≡ Ωb h 2 = 0.0224 ± 0.0009, ω m ≡ Ω m h 2  ΔH 2                  Δω b ...
WMAP 5 & 7: Angular power spectrum                              3rd                             peak                      ...
Current Angular power spectrum                                          3rd                                         peak  ...
Ω00m + Ω Λ + Ω0 K + Ω0 r = 1     Ω m + ΩΛ +Image Credit: NASA / WMAP Science Team                                         ...
Good old Cosmology, … New trend !                         Total energy                           density                  ...
Non-Parametric: Peak Location         (Amir Aghamousa, Mihir Arjunwadkar,  TS  ApJ 2012)
Implied ‘cosmological parameter’ estimation         (Amir Aghamousa, Mihir Arjunwadkar,  TS, in progress, 2012)
Non-Parametric fit to CMB spectrum     (Amir Aghamousa, Mihir Arjunwadkar,  TS  in progress)
Statistics of CMBCMB Anisotropy Sky map => Spherical Harmonic decomposition                                      ∞     l  ...
Beyond Cl :   Detecting patterns in CMB Universe on Ultra-Large scales:   • Global topology   • Global anisotropy/rotation...
‘Anomalies’ in the WMAP CMB mapsNorth-South asymmetryEriksen, et al. 2004,2006; Hansen et al. 2004 (in local power)Larson ...
Statistics of CMB                 C(n1 , n2 ) ≡ C(n1 • n2 )                   ˆ ˆ           ˆ ˆPossibilities:•   Statistic...
f ( n ) ≡ C ( n, z )                                                     ˆ         ˆ ˆRadical breakdown of SI  disjoint is...
Beautiful Correlation patterns                 could underlie the CMB tapestry    Can we measure correlation patterns?Figs...
Measuring the SI correlation               Statistical isotropy                   C (θ )  can be well estimated           ...
Measuring the non-SI correlation     In the absence of statistical isotropy     Estimate of the correlation function from ...
Bipolar Power spectrum (BiPS) :      A Generic Measure of Statistical Anisotropy                                          ...
⇒κ =κ δ                                                                     0 Statistical Isotropy                        ...
Bipolar Power spectrum (BiPS) :    A Generic Measure of Statistical Anisotropy• Correlation is a two point function on a s...
Recall: Coupling of angular momentum states   l1m1l2 m2 | M   l1 − ≤ l2 ≤ l1 + , m1 + m2 + M = 0  BiPoSH         Al1l2 = ∑...
Understanding BiPoSH SI violation:                                    coefficients   alm al* m  ≠ Cl δ ll δ mm            ...
Spherical         Bipolar spherical    harmonics             harmonics                             M         alm          ...
Spherical     Bipolar spherical         harmonics         harmonics                               M             alm       ...
BIPOLAR maps of WMAP  Hajian & Souradeep (PRD 2007)                          ILC-3Reduced BipoSH                          ...
Is the Universe Compact ?                                       Simple Torus                                       (Euclid...
BiPS signature of a “soccer ball” universe             (Hajian, Pogosyan, TS, Contaldi, Bond : in progress.)              ...
BiPS signature of a “soccer ball” universe              (Hajian, Pogosyan, TS, Contaldi, Bond :              in progress.)...
BiPS signature of Flat Torus spaces               BiPS      Spectroscopy ofκ                 Cosmic topology     !?!      ...
Spaces that have must have only        Even multipole BiPS ?  Flat compact spaces  Single-action spherical compact spacesr...
BIPOLAR measurements by WMAP-7 team ( + ) LM                                                             (Bennet et al. 20...
Statistical Isotropy: CMB Photon distribution                                       (Moumita Aich & TS, PRD 2010) Δ ( x , ...
Statistical Isotropy: CMB Photon distribution                                            (Moumita Aich & TS, PRD 2010)    ...
Even & odd parity BipoSH        A l(2+1 ) L M = A l(1 l+2 ) L M             l                                        s y m...
Weak Lensing
SI violation : Deflection field                          ˆ                          n                                    ˆ...
Deflection field: Even & Odd parity BipoSH           Book, Kamionkowski & Souradeep, PRD 2012                        ⎡ Cl ...
BipoSH Measures of deflection fieldEstimators                                                         Variance        ∑Q A...
WMAP-7 BIPOLAR ‘anomaly’ from weak lensing?  ϕ20∼ 0.02    (Aditya Rotti, Moumita Aich & TS arXiv:1111.3357)
Implications :• The quadrupole of the projected lensing potential is large and cannot  be accomodated in the standard LCDM...
• To probe violations of isotropy, measuring the large scale    distribution of dark matter surrounding us will be of utmo...
Status of Non-GaussianityMild 2.5σ deviation hinted in the WMAP 3 data !                  Yadav & Wandelt (2008); Smith, S...
CMB BipoSHs & Bispectra                                              (Kamionkowski & Souradeep, PRD 2011)For deflection fi...
Odd parity Bispectra ?                    (−                   BLll ) ∼   ∑                                M              ...
Odd parity BispectraFor local NG model                                                                                    ...
Planck Surveyor SatelliteEuropean Space Agency: Launched May 14, 2009 HFI completed Jan 2012               Planck Satellit...
Summary•   Current observations now allow a meaningful search for deviations from the `standard’    flat, ΛCDM cosmology.•...
Ultra Large scale structure of the universe       Thank you !!!
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  1. 1. Challenging the Isotropic CosmosCTACC Colloquium Tarun Souradeep AIMS, Cape Town I.U.C.A.A, Pune, India (Apr. 13, 2012)
  2. 2. CMB space missions1991-94 2001-2010 2009-2011 CMBPol/COrE 2020+
  3. 3. Cosmic Microwave BackgroundPristine relic of ahot, dense & smoothearly universe -Hot Big Bang modelPost-recombination :Freelypropagating through (weaklyperturbed) homogeneous &isotropic cosmos.Pre-recombination : Tightlycoupled to, and in thermalequilibrium with, ionizedmatter. (text background: W.
  4. 4. Cosmic “Super–IMAX” theater 0.5 Myr Here & Now (14 Gyr) Transparent universe Opaque universe
  5. 5. CMB Anisotropy & Polarization CMB temperature Tcmb = 2.725 K -200 μ K < Δ T < 200 μ K Δ Trms ~ 70μ K ΔTpE ~ 5 μ K ΔTpB ~ 10-100 nK Temperature anisotropy T + two polarization modes E&B Four CMB spectra : ClTT, ClEE,ClBB,ClTE Parity violation/sys. issues: ClTB,ClEB
  6. 6. Statistics of CMBCMB Anisotropy Sky map => Spherical Harmonic decomposition ∞ l Δ T (θ , φ ) = ∑ ∑a Y (θ , φ ) lm lm l =2 m=− l alm a * l m = Cl δ ll δ mm Gaussian Random field => Completely specified by angular power spectrum l(l+1)Cl : Power in fluctuations on angular scales of ~ π/l
  7. 7. Fig. M. White 1997 The Angular power spectrum of CMB anisotropy depends C sensitively on Cosmological l parameters Hence, a powerful tool for constraining cosmological parameters.Multi-parameter Joint likelihood (MCMC)
  8. 8. Dissected CMB Angular power spectrum •Low multipole : • Moderate multipole : • High multipole :Sachs-Wolfe plateau Acoustic “Doppler” peaks Damping tail CMB physics is very well understood !!! (fig credit: W. Hu)
  9. 9. Cosmic Acoustics: Ping the ‘Cosmic drum’ 150 Mpc More technically, (Fig: Einsentein ) the Green function
  10. 10. WMAP: Angular power spectrumIndependent, self contained analysis of WMAP multi-frequency maps Saha, Jain, Souradeep (WMAP1: Apj Lett 2006) WMAP3 2nd release : TS,Saha, Jain: Irvine proc.06 Eriksen et al. ApJ. 2006 Good match to WMAP team
  11. 11. Peaks of the angular power spectrum (74.1±0.3, 219.8±0.8) (74.7 ±0.5, 220.1 ±0.8 Ω0K = 0 Ω0 B = 0.04 (48.3 ±1.2, 544 ±17) (48.8 ±0.9, 546 ±10) (41.7 ±1.0, 419.2 ±5.6) (41.0 ± 0.5, 411.7 ±3.5) (Saha, Jain, Souradeep Apj Lett 2006)
  12. 12. Peak heights and ratios Cosmological Parametersωb ≡ Ωb h 2 = 0.0224 ± 0.0009, ω m ≡ Ω m h 2 ΔH 2 Δω b Δω m = 0.88Δns − 0.67 + 0.04 H2 ωb ωm ΔH 3 Δω b Δω m = 1.28Δns − 0.39 + 0.46 H3 ωb ωm ΔH 2 TE Δω b Δω m = −0.66Δns + 0.095 + 0.45 H2 TE ωb ωm
  13. 13. WMAP 5 & 7: Angular power spectrum 3rd peak Fig.: Tuhin Ghosh
  14. 14. Current Angular power spectrum 3rd peak 4th peak 5th peak 6thpeakImage Credit: NASA / WMAP Science Team
  15. 15. Ω00m + Ω Λ + Ω0 K + Ω0 r = 1 Ω m + ΩΛ +Image Credit: NASA / WMAP Science Team Fig.: Moumita Aich
  16. 16. Good old Cosmology, … New trend ! Total energy density Dark energy Baryonic matter density density ‘Standard’ cosmological model: Flat, ΛCDM (with nearly Power Law primordial power spectrum)NASA/WMAP science team
  17. 17. Non-Parametric: Peak Location (Amir Aghamousa, Mihir Arjunwadkar,  TS  ApJ 2012)
  18. 18. Implied ‘cosmological parameter’ estimation (Amir Aghamousa, Mihir Arjunwadkar,  TS, in progress, 2012)
  19. 19. Non-Parametric fit to CMB spectrum (Amir Aghamousa, Mihir Arjunwadkar,  TS  in progress)
  20. 20. Statistics of CMBCMB Anisotropy Sky map => Spherical Harmonic decomposition ∞ l Δ T (θ , φ ) = ∑ ∑a Y (θ , φ ) lm lm l =2 m=− l Gaussian CMB anisotropy completely specified by the angular power spectrum IF Statistical alm a * = Cl δ ll δ mm isotropy l m =>Correlation function C(n,n’)=<ΔT(n) ΔT(n’)> is Rotationally Invariant
  21. 21. Beyond Cl : Detecting patterns in CMB Universe on Ultra-Large scales: • Global topology • Global anisotropy/rotation • Breakdown of global syms, Magnetic field,… Deflection fieldsObservational artifacts:• Foreground residuals• Inhomogeneous noise, coverage• Non-circular beams (eg., Hanson et al. 2010)
  22. 22. ‘Anomalies’ in the WMAP CMB mapsNorth-South asymmetryEriksen, et al. 2004,2006; Hansen et al. 2004 (in local power)Larson & Wandelt 2004 … , Park 2004 (genus stat.) Cosmic topology. (Poincare Dodecahedron).Special directions (“Axis of Evil”)Tegmark et al. 2004 (l=2,3 aligned), 2006Copi et al. 2004 (multipole vectors), … ,2006Land & Magueijo 2004 (cubic anomalies), …Prunet et al., 2004 (mode coupling)Bernui et al. 2005 (separation histogram)Wiaux et al. 2006 Anisotropic, rotating cosmosUnderlying patterns (Bianchi VIIh)T.Jaffe et al. 2005,2006.. Statistical properties are not invariant under rotation of the sky Breakdown of Statistical Isotropy !
  23. 23. Statistics of CMB C(n1 , n2 ) ≡ C(n1 • n2 ) ˆ ˆ ˆ ˆPossibilities:• 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
  24. 24. f ( n ) ≡ C ( n, z ) ˆ ˆ ˆRadical breakdown of SI disjoint iso-contours multiple imagingMild breakdown of SIDistorted iso-contours Statistically isotropic (SI) Circular iso-contoursE.g.. Compact hyperbolic Universe . (Bond, Pogosyan & Souradeep 1998, 2002)
  25. 25. Beautiful Correlation patterns could underlie the CMB tapestry Can we measure correlation patterns?Figs. J. Levin the COSMIC CATCH is
  26. 26. Measuring the SI correlation Statistical isotropy C (θ ) can be well estimated by averaging over the temperature product between all pixel pairs separated by an angle θ . ~ C(θ ) = ∑∑ΔT (n1)ΔT (n2 )δ (n1 ⋅ n2 − cosθ ) ˆ n1 ˆ n2 1 C (n1 • n2 ) = ˆ ˆ 8π 2 ∫ dℜ C (ℜn1 , ℜn2 ) ˆ ˆ
  27. 27. 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 ~ C ( n1 , n 2 ) = Δ T ( n1 ) Δ T ( n 2 ) 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)
  28. 28. Bipolar Power spectrum (BiPS) : A Generic Measure of Statistical Anisotropy 1 Recall : C (n1 • n2 ) = 2 ∫ dℜ C (ℜn1 , ℜn2 ) ˆ ˆ ˆ ˆBipolar multipole index 8π 2 ⎡ 1 ⎤ κ = ∫ dΩ n ∫ d Ω n 1 2 ⎢ 8π 2 ∫ dℜ χ (ℜ) C (ℜn1 , ℜn2 )⎥ ⎣ ˆ ˆ ⎦ A weighted average of the correlation function over all χ (ℜ ) = ∑D m=− mm (ℜ ) rotations Wigner Characteristic function rotation matrix
  29. 29. ⇒κ =κ δ 0 Statistical Isotropy 0 Correlation is invariant under rotations C (ℜn1 , ℜn2 ) = C (n1 , n2 ) ˆ ˆ ˆ ˆ 1κ = (2 + 1) ∫ dΩ ∫ dΩ ∫ dℜ χ 2 2 2 n1 n2 ˆ ˆ C (n1 , n2 )[ (ℜ)] 8π 2 ∫ dℜχ (ℜ) = δ 0
  30. 30. Bipolar Power spectrum (BiPS) : A Generic Measure of Statistical Anisotropy• Correlation is a two point function on a sphere BiPoSH C ( n1 , n2 ) = ∑A l1l2 LM LM l1l2 {Yl1 ( n1 ) ⊗ Yl2 ( n2 )}LM Bipolar spherical harmonics. C (n1 • n2 ) = ∑ 2l + 1 Cl Pl (n1 • n2 ) {Yl1 (n1 ) ⊗ Yl2 (n2 )}LM = ∑ Cl1l2m1m2Yl1m1 (n1 )Yl2m2 (n2 ) 4π LM• Inverse-transform m1m2 Clebsch-Gordan Al1l2 = ∫ dΩn1 ∫ dΩn2C(n1, n2 ){Yl1 (n1) ⊗Yl2 (n2 )}* LM LM = ∑ al1m1al2m2 Cl1m1l2m2 LM Linear combination of off-diagonal elements m1m2
  31. 31. Recall: Coupling of angular momentum states l1m1l2 m2 | M l1 − ≤ l2 ≤ l1 + , m1 + m2 + M = 0 BiPoSH Al1l2 = ∑ al1m1 al2 M +m1 M * M Cl1m1l2 M +m1 coefficients : m1• 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 : D l ≡ a lm a l + 2 m = ∑ All M C l +M m l m M 2 Dl( i ) ≡ alm al +1 m+i = ∑ A Cl +M m+i l m M ll 1 M BiPS: rotationally invariant κ ≡ ∑| A M ,l1 ,l2 M 2 l1l2 | ≥0
  32. 32. Understanding BiPoSH SI violation: coefficients alm al* m ≠ Cl δ ll δ mm 4M A ll 2MAll = ∑ LM alm al m LM C lml m A ll mm Measure cross correlation in alm
  33. 33. Spherical Bipolar spherical harmonics harmonics M alm All Spherical Harmonic BiPoSH coefficents coefficents Cl κ Angular power BiPS spectrumBipolar Power spectrum (BiPS) :A Generic Measure of Statistical Anisotropy
  34. 34. Spherical Bipolar spherical harmonics harmonics M alm All Spherical Harmonic BipoSH Transforms Transforms Cl κ Angular power BiPS spectrumStatistical Isotropy ⇒ κ = κ δ 0 i.e., NO Patterns 0
  35. 35. BIPOLAR maps of WMAP Hajian & Souradeep (PRD 2007) ILC-3Reduced BipoSH Bipolar representationAM = ∑ • M All Measure of statistical isotropy ll • Spectroscopy of Cosmic topology ILC-1 Visualizing non-SI • Anisotropic power spectrumBipolar map correlations • Deflection fields (WL,…) • Diagnostic of systematic effects/observational ∑ artifacts in the mapθ ( n ) = •A Differentiate Cosmic vs. Galactic B-mode Diff. ˆ M Y M (n) ˆ M polarization•SI part corresponds to the“monopole” of the map.
  36. 36. Is the Universe Compact ? Simple Torus (Euclidean) Multiply connected Spherical space (Poincare dodecahedron) Compact hyperbolic space Post WMAP Nature article (Luminet et al 2003)
  37. 37. BiPS signature of a “soccer ball” universe (Hajian, Pogosyan, TS, Contaldi, Bond : in progress.) ΩK = Ideal, noise free maps predictionsκ
  38. 38. BiPS signature of a “soccer ball” universe (Hajian, Pogosyan, TS, Contaldi, Bond : in progress.) Ωtot = 1.013 Ideal, noise free mapsκ predictions
  39. 39. BiPS signature of Flat Torus spaces BiPS Spectroscopy ofκ Cosmic topology !?! Hajian & Souradeep (astro- ph/0301590)
  40. 40. Spaces that have must have only Even multipole BiPS ? Flat compact spaces Single-action spherical compact spacesr No hyperbolic compact spacesHM, TS: Discussion with JeffWeeks
  41. 41. BIPOLAR measurements by WMAP-7 team ( + ) LM (Bennet et al. 2010)Al1l2 L0 Non-zero Bipolar coeffs.!!!C l 0 l 0 9‐σ Detections !! Sys. effect : beam distortion ? (Souradeep & Ratra 2000, Mitra etal 2004, 2009 Hanson et al. 2010, Joshi, Mitra, TS 2012)Image Credit: NASA / WMAP Science Team
  42. 42. Statistical Isotropy: CMB Photon distribution (Moumita Aich & TS, PRD 2010) Δ ( x , p,τ ) ˆ ⎯⎯→FT Δ ( k , p, τ ) ≡ Δ ( k , k , p, τ ) ˆ ˆ ˆ Δ(k , k , p,τ ) ≡ Δ(k , k • p,τ ) ˆ ˆ ˆ ˆ Δ(k , k , p,τ ) SH ↓ Expansion ˆ ˆ Bipolar ≡ Δ ( k , k • p,τ ) ˆ ˆ ↓ Expansion LegendreΔ LM (k ,τ ) Δ ( k ,τ ) dk = ∫ P(k ) ∑ Δ 1 (k2 τ o ) ⎡Δ 1 (k ,τ o ) ⎤ * LM LM a ma m dk , ⎣ ⎦ C ∫ LML( M ) 1Δ (k ,τ ) k= P k m1 k × C LM1 m C L1m1 m 1m M
  43. 43. Statistical Isotropy: CMB Photon distribution (Moumita Aich & TS, PRD 2010) Δ (k ,τ rec ) ⎯⎯⎯⎯ Δ (k ,τ 0 ) → Free streamStatistical ∑ [...] j (k Δτ ) 2 isotropy = l ⎡C ⎣ l0 0 0 ⎤ Δ (k ,τ rec ) ⎦ l Δ LM4 (k ,τ rec ) 3 ⎯⎯⎯⎯ Δ L1M2 (k ,τ 0 ) Free stream →General: ⎧ L ⎫ Non- = ∑ [...] j (k Δτ ) C l L0 0 10 C L0 0 10 ⎨ 4 3 ⎬Statistical 3 4 ⎩ 1 l 2 ⎭ isotropy × Δ LM4 (k ,τ rec ) 3
  44. 44. Even & odd parity BipoSH A l(2+1 ) L M = A l(1 l+2 ) L M l s y m m e tric A l(2−1 ) L M = − A l(1 l−2 ) L M l a n tis y m m .[ A l(1 l+2 ) L M ]* = ( − 1) M A l(1 l+2 ) L , − M E v e n p a rity[ A l(1 l−2 ) L M ]* = ( − 1) M + 1 A l(1 l−2 ) L , − M O d d p a rit y
  45. 45. Weak Lensing
  46. 46. SI violation : Deflection field ˆ n ˆ n T (n ) = T (n + Θ) = T ( n ) + Θ • ∇T ( n ) ˆ ˆ ˆ ˆoo Θ = ∇φ ( n ) + ∇ × Ω ( n ) ˆ ˆ = ∇iφ ( n ) + ε ij ∇ j Ω( n ) ˆ ˆ Gradient Curl WL:scalar WL: tensor/GW
  47. 47. Deflection field: Even & Odd parity BipoSH Book, Kamionkowski & Souradeep, PRD 2012 ⎡ Cl GlL l Cl Gll ⎤ L All+ ) LM = φLM ( ⎢ + ⎥ WL: scalar ⎣ l (l + 1) l (l + 1) ⎦ ⎡ Cl GlL l Cl Gll ⎤ WL: tensor L Al(2−1) LM = iΩ LM ⎢ − ⎥ ⎣ l (l + 1) l (l + 1) ⎦ l
  48. 48. BipoSH Measures of deflection fieldEstimators Variance ∑Q A + ( + ) LM /σ 2 LM ⎡ 2 LM ⎤ −1 ( ) ll ll ll φLM = ll var φLM = ⎢ ∑ (Qll ) / σ ll ⎥ + 2 ∑ (Q ) ll + 2 ll /σ 2 LM ll ⎣ ll ⎦ ∑ Qll All− ) LM / σ ll LM − ( 2 −1 ⎡ 2 LM ⎤Ω LM = var ( Ω LM ) = ⎢ ∑ (Qll ) / σ ll ⎥ ll − 2 ∑ (Qll ) 2 / σ ll LM − ll 2 ⎣ ll ⎦ ( ± ) LM ( ± ) LM A A A ( ± ) LM l1l2 → l1l2 L1 [...] = l1l2 L C l 0 l 1 G ll
  49. 49. WMAP-7 BIPOLAR ‘anomaly’ from weak lensing? ϕ20∼ 0.02 (Aditya Rotti, Moumita Aich & TS arXiv:1111.3357)
  50. 50. Implications :• The quadrupole of the projected lensing potential is large and cannot be accomodated in the standard LCDM cosmology.• The BipoSH detection could be suggesting a strong deviation from standard cosmology. Primordial non-Gaussianity / alternative theories of gravity could possibly explain the large value of the quadrupole.
  51. 51. • To probe violations of isotropy, measuring the large scale distribution of dark matter surrounding us will be of utmost importance.• Making measurements of the LSS on the largest angular scales will be an extremely challenging task. However future experiments like LSST, DES and EUCLID might make this possible. Lewis and
  52. 52. Status of Non-GaussianityMild 2.5σ deviation hinted in the WMAP 3 data ! Yadav & Wandelt (2008); Smith, Senatore and Zaldarriaga 2009) WMAP5&7 consistent with zero Slide adapted from Amit Yadav
  53. 53. CMB BipoSHs & Bispectra (Kamionkowski & Souradeep, PRD 2011)For deflection field alm = alm + δ alm S All ∼ φLM ∑ alm als m Clml m LM s LM mm φ LM → a LM ⇒ All ∼ ∑ aLM alm al m Clmlm LM LM mm BipoSH related to Bispectrum BLll ∼ ∑ Mmm LM aLM alm al m Clml m (...) ∼ ∑A M ( + ) LM ll Consider only: l + l + L = even
  54. 54. Odd parity Bispectra ? (− BLll ) ∼ ∑ M All− ) LM (Flat sky intuition: l2 l2 l3 l3 l1 < l2 < l3 l1 l1 (−) l1 × l2 has opposite sign in the B ∼ two mirror configurations. l1l2
  55. 55. Odd parity BispectraFor local NG model Flat sky approx ⎡ odd l1 × l2 ⎤B(l1 , l2 ) = 2 ⎢ f nl + f nl ⎥ (Cl1 Cl2 + perms. ) ⎣ l1l2 ⎦ In general (Cl1 Cl2 + ) ∑ perms. f nl = σ 2 6G l3 Ell13l2 Cl1 Cl2 + Cl3 Cl2 + Cl1 Cl3 f nl l1l2 l1 <l2 <l3 (Cl1 Cl2 + ) ∑ perms. f odd = σ 2 6G l3 Oll13l2 Cl1 Cl2 + Cl3 Cl2 + Cl1 Cl3 nl f nl l1l2 l1 <l2 <l3 2 ⎡6 G (Cl1 Cl2 + perms.) ⎤ l3 σ −2 = ∑ ⎣ ⎦ l1l2 l1 <l2 <l3 Cl1 Cl2 + Cl3 Cl2 + Cl1 Cl3 f nl
  56. 56. Planck Surveyor SatelliteEuropean Space Agency: Launched May 14, 2009 HFI completed Jan 2012 Planck Satellite on display at Cannes, France (Feb. 1, 2007) Capabilities: •3x angular resolution of WMAP •5 to 20 x sensitivity of WMAP Promises: • Cosmic Variance limited primary ClTT • Polarization ClEE as good WMAP ClTT • Unlikely, but may be lucky with ClBB • Planck HFI core team members @IUCAA working on SI measurements using BipoSH (Sanjit Mitra, Rajib Saha, TS)
  57. 57. Summary• Current observations now allow a meaningful search for deviations from the `standard’ flat, ΛCDM 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. – BipoSH provide a well structured representation of the systematic breakdown of rotational symmetry. – Bipolar observables have been measured in the WMAP data.• 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.
  58. 58. Ultra Large scale structure of the universe Thank you !!!
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