Evidence for Large Scale Anisotropy in the Universe

1. Evidence for Large Scale Anisotropy in the Universe Pankaj Jain I.I.T. Kanpur

2. Introduction • Universe is known to be isotropic at large distance scales For example, CMB is highly isotropic • However there are some indications of anisotropy in several data sets • Radio polarizations from radio galaxies • Optical polarizations from quasars • CMB anisotropies

3. Anisotropy in Radio Polarizations Radio Polarizations from distant AGNs show a dipole anisotropy • Offset angle b = c - y • q(l2 ) = c + (RM) l2 RM : Faraday Rotation Measure c = IPA (Polarization at source)

4. Anisotropy in Radio Polarizations cut |RM - <RM>| > 6 rad/m2 averaged over a small region preferred axis points towards Virgo Birch 1982 Jain, Ralston, 1999 Jain, Sarala, 2003 beta = polarization offset angle = polarization angle – galaxy alignment angle

5. Rotation Measure Cut

6. DATA The data consists of all the radio sources for which the observables , , RM exist in the literature

7. Statistical Significance using Likelihood Analysis Full Data: (332 sources) P = 3.5 % Using cut: |RM - <RM>| > 6 (265 sources) P = 0.06 %

8. The signal was first noticed by Birch in 1982 • It was dismissed by Bietenholz and Kronberg (BK) in 1984 using a larger data set • However BK did not test for the signal that Birch found • The signal is parity odd whereas BK tested for a signal with mixed parity (Jain and Ralston 1999)

9. HutsemékersEffect Optical Polarizations of QSOs appear to be locally aligned with one another. (Hutsemékers, 1998) 1<z<2.3 A very strong alignment is seen in the direction of Virgo cluster

10. Preferred Axis Two point correlation Define the correlation tensor Define where S is a unit matrix for an isotropic uncorrelated sample is the matrix of sky locations

11. Optical Polarizations Preferred axis points towards to Virgo Ralston and Jain, 2004 Degree of Polarization < 2%

12. Cosmic Microwave Background Radiation (CMBR) CMBR is highly isotropic It shows a dipole anisotropy with This arises due to motion of our galaxy The higher order multipoles arise due to primordial fluctuations

13. DT(q,f) = Temperature Fluctuations about the mean Two Point Correlation Function Statistical isotropy implies

14. In harmonic space, statistical isotropy implies estimate of Cl :

15. Very high resolution multi-frequency CMB data is available from WMAP The data is contaminated: foregrounds (emissions from our galaxy) detector noise (dominant at high multipoles l ) extragalactic point sources (dominant at high l)

16. WMAP multi-frequency maps Ka band 33 GHz K band 23 GHz Q band 41 GHz W band 94 GHz V band 61 GHz

17. WMAP Internal Linear Combination (ILC)

19. The power at l=2 is low in comparison to the best fit CDM model. This may be explained in terms of a negative bias in the extracted power at low l (Saha et al 2008)

20. CMB anisotropies also give an indication of large scale anisotropy Quadrupole and octopole show a preferred axis pointing towards Virgo Oliveira-Costa et al 2003

21. Quadrupole Octopole

22. CMB dipole also points towards Virgo Oliveira-Costa et al 2003 Ralston and Jain, 2004 Schwarz et al 2004 Hence we find several diverse data sets, all indicating a preferred axis pointing towards Virgo Ralston and Jain, 2004

23. Prob. for pairwise coincidences Ralston and Jain, 2004

24. The Virgo Alignment optical quadrupole and octopole radio dipole

25. Axis of Evil The axis is some times called the Axis of Evil I think this name is inappropriate It does not provide any description of the phenomenon The term ‘evil’ suggests that the phenomenon is undesired Such sentiments may be relevant in religion but not in science

26. Alternate Title The Virgo Axis The Virgo Alignment

27. Hemispherical Power Asymmetry Eriksen et al, 2004, 2007 Try to determine if the extracted power is anisotropic Model CMB temperature fluctuations as, T(,) = s(,) [1+ f(,)] + n(,) detector noise dipole modulation field Statistically isotropic field

28. Eriksen et al claim dipole modulation amplitude = 0.114 P<1% for this amplitude to arise in an isotropic universe

29. A Cold Spot in CMB data Cruz et al (2004) claim existence of a cold spot of size about 10o at (l, b) = (209o,  57o) This is detected using Spherical Mexican Hat Wavelet Analysis with chance Probability 0.2%

30. The Axis of Anisotropy Dipole modulation axis Cold spot

31. Zhang and Huterer (2009) do not find significant signal for the presence of the cold spot The difference arises due to their use of circular top hat weights and Gaussian weights instead of Spherical Mexican Hat Wavelets  outcome depends on the choice of the basis wavelet functions

32. Large Scale Coherent Flow Peculiar velocity distribution of clusters indicates a large scale bulk flow at distance scales of order 800 Mpc For z  0.25, axis (l,b) = (296  29, 39  15)o Kashlinsky et al 2008, 2009

33. A Dipole Anisotropy in Galaxy Distributions Itoh et al (2009) claim evidence for dipole anisotropy in the galaxy distribution using SDSS data The amplitude is an order of magnitude larger than expected due to solar motion

34. The Axis of Anisotropy Galaxy distribution Peculiar velocity

35. High z Supernova Data • One may also search for anisotropy using Supernova data • Violation of isotropy is found, but can be attributed to selection effects • At low significance we find anisotropy with an axis lying in the galactic plane (Jain, Modgil, Ralston 2005) • This might indicate a bias in the extinction corrections • Bias in supernova data was found (Jain, Ralston 2004)

36. High z Supernova Data • Cooke and Lynden-Bell (2009) find a signal with very low significance with axis roughly towards CMB dipole

37. General Procedures to test for violation of statistical isotropy in CMB

38. Bipolar Power Spectrum (BiPS) Bipolar spherical harmonics coefficients = Clebsch-Gordon coeffs Spherical Harmonics Hajian and Souradeep, 2003, 2005

39. Bipolar Power Spectrum (BiPS) Statistical Isotropy  In order to test for Statistical Isotropy, define Statistical Isotropy  L= 0  L > 0

40. Hajian and Souradeep do not find any violation of isotropy They search over several different multipole ranges by employing a window function

41. Copi et al, 2004, 2006, 2007 proposed a test of statistical isotropy by constructing l unit vectors for each multipole l. This is closely related to a method we introduced. We associate a covariant frame (3 orthogonal unit vectors) with each multipole l. This characterizes the preferred direction for each multipole. Ralston and Jain, 2004 Samal, Saha, Jain and Ralston 2008

42. Covariant Frames Using Dirac notation : are eigenvectors of angular momentum operator define a linear map or wave function: = angular momentum operators

43. Singular value decomposition   are the singular values The set of three orthogonal e defines a preferred frame for the multipole l

44. Power Entropy : We define a density matrix We associate an entropy with this matrix Von Neumann (1932) isotropy  S = log(3)

45. Power entropy is useful to test for anisotropy in a particular multipole l Once we have the preferred frames for each l, we can test for alignment of frames among different l

46. Alignment across different l-multipoles we construct a matrix X defined by : is the “principal axis”, which means the eigenvector with largest eigenvalue for each l Isotropy for a range of multipole moments can be tested with the alignment entropy: is the normalized X matrix.

47. The eigenvector of X corresponding to maximum eigenvalue gives the preferred direction in the chosen multipole range

48. Using this technique we may test for anisotropy at any multipole value or in a range of multipole values However we need to account for the search over the multipole range in assigning statistical significance Due to the large number of possibilities one should interpret the signal seen in any particular range with caution

49. Results (ILC map, 2  l  50) • We find significant signal of anisotropy (at 2 sigma) using power entropy • We find signal for alignment with quadrupole at 2 sigma

50. Higher l multipoles 2  l  300 Here we test for anisotropy using the individual foreground cleaned DAs Q1, Q2, V1, V2, W1, W2, W3, W4 We use maps with Kp2 mask