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.  Offset angle      RM)  Anisotropy in Radio Polarizations Radio Polarizations from distant AGNs show a dipole anisotropy RM : Faraday Rotation Measure  = IPA (Polarization at source)

4. Anisotropy in Radio Polarizations cut |RM - | > 6 rad/m 2 beta = polarization offset angle = polarization angle – galaxy alignment angle Birch 1982 Jain, Ralston, 1999 Jain, Sarala, 2003 preferred axis points towards Virgo averaged over a small region

5. Rotation Measure Cut

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

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

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

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

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

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

13.  T  Temperature Fluctuations about the mean Statistical isotropy implies Two Point Correlation Function

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

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

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

23. dipolequadoctoradiooptical dipole0.0200.0610.0420.024 quad0.0150.0230.004 octo0.0590.026 radio0.008 Prob. for pairwise coincidences Ralston and Jain, 2004

24. The Virgo Alignment quadrupole and octopole dipole radio optical

25. 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 Axis of Evil

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( ,  ) Statistically isotropic field dipole modulation field detector noise

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 10 o at (l, b) = (209 o,  57 o ) This is detected using Spherical Mexican Hat Wavelet Analysis with chance Probability 0.2%

30. The Axis of Anisotropy Cold spot Dipole modulation axis

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) Hajian and Souradeep, 2003, 2005 Bipolar spherical harmonics coefficients = Clebsch-Gordon coeffs Spherical Harmonics

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

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

44. Power Entropy : We associate an entropy with this matrix We define a density 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

51. Results (2  l  300, 150  l  300) We find signal of strong anisotropy in the Q1 and Q2 DAs. The axis of alignment lies at galactic latitude b=25 o Hence it most likely arises due to unknown residual foregrounds We do not find signal of alignment with quadrupole in this range in any DA

52. The DAs V1, W1, W2, W3 instead show an improbable degree of isotropy with P  0.75%, 0.02 %, 0.01%, 0.01% (150  l  300, using alignment entropy) We do not understand the cause of this. It may be due to incorrect modeling of detector noise. The problem disappears if we reduce detector noise by about 25%

53. We have also applied our analysis to the foreground cleaned polarization maps (2  l  300) We find a very strong signal in almost all the DAs The axis points in the same direction as the axis found for Q-band temperature maps. We found that the signal disappears if we enhance the mask applied to the data. However the axis continues to point in the same direction

54. The Axis of Anisotropy

55. Physical Interpretation

56. There appears to be several indications of anisotropy There does not exist a model which explains all the data

57. Physical Interpretation The effect could be consistent with standard  CDM model if it arises due to some unknown local effect Alternatively the phenomenon represents a violation of the cosmological principal I don’t see anything wrong with this but it would lead to a serious increase in the amount of work for theoreticians

58. Physical Interpretation There is no reason that the early universe is isotropic and homogeneous It might approach isotropy and homogeneity as it expands In this case one cannot rule out a small violation of the cosmological principle.

59. Violation of Lorentz Invariance Lorentz invariance may be violated due to quantum gravity effects (Collins et al 2004) The violation is found to be rather large suggesting a fine tuning problem The fine tuning problem is avoided if one imposes SUSY. In this case the violation is found to be of order (M SUSY /M PL ) 2 (Jain and Ralston 2005)

60. Physical explanations for violation of isotropy Galactic foregrounds Supercluster foregrounds Anisotropic metric Inhomogeneous metric Spontaneous violation of isotropy Local Rees-Sciama effect Anisotropic cosmological constant Anisotropic inflation, perhaps due to a vector field Voids in our astrophysical neighbourhood Magnetic field leading to anisotropic metric Pseudoscalar-photon mixing in background magnetic field Rotating universe …

61. Galactic Foregrounds unknown foreground effects may explain the CMB anisotropies This may be a good explanation if the axis lies close to the galactic plane and might explain the anisotropy at high l (Samal et al 2008) as well as the dipole modulation effect (Eriksen et al 2004)

62. Galactic Foregrounds alignment of quadrupole and octopole may also arise due to Galactic foregrounds. Removing the most contaminated part of the data removes any evidence of alignment ( Slosar and Seljak (2005)) not very surprising

63. Quadrupole Octopole Hot and cold spots lie close to galactic plane

64. Supercluster Foregrounds Abramo et al (2008) argue that supercluster foregrounds in the vicinity of CMB dipole axis can explain the alignment This can increase the quadrupole power and reduce the significance of alignment of quad and octo The foreground might arise due to Sunyaev- Zeldovich effect due to hot electrons in the local supercluster

65. Local Voids The presence of local voids at some select positions may explain the CMB anomalies Dust filled void of radius 300 h  1 Mpc,  =  0.3 leads to a cold spot  T/T ~  10  5 (Inoue and Silk 2008)

66. Inhomogeneous Universe An inhomogeneous metric could lead to large scale CMB anisotropies. For example, it will lead to different power in different hemispheres In this case one may also need to re-interpret the deceleration parameter (Moffat 2005) This is also likely to produce an anisotropy in the supernova data

67. Spontaneous Breakdown of Isotropy Isotropy is broken locally by the gradient of a scalar field whose spatial fluctuations are dominated by long wavelength contributions The gradient picks a particular direction and breaks isotropy locally The long wavelength mode produces inhomogeneity which leads anisotropy in CMB (Gordon et al 2005)

68. Superhorizon Mode Erickcek et al (2008)

69. Inflation in Inhomogeneous Universe Gordon (2007), Erickcek et al (2008) explain the observed hemispherical power asymmetry using this idea. They argue that a two scalar field inflationary model can produce the required asymmetry without violating constraints on homogeneity of Universe.

70. Asymmetric Expansion Berera et al (2004) obtain anisotropic expanding universe in the presence of cosmological constant and uniform background magnetic field (or strings or domain walls) Inflation might push all but one magnetic field domain outside the horizon  uniform magnetic field Buniy et al (2006) obtain anisotropic inflationary solutions in such a universe

71. Anisotropic inflation with non-standard spinor Spin half field with mass dimension 1 proposed as a dark matter candidate (Ahluwalia-Khalilova and Grumiller, 2005) Bohmer and Mota (2008) show that inflation driven by a elko spinor is anisotropic Elko spinor

72. Dipole Anisotropy in Radio Polarizations It might arise due to propagation, provided Maxwell’s equations are suitably modified. It can arise due to: Explicit or spontaneous violation of Lorentz invariance (Carroll et al 1990, Nodland and Ralston 1997, Andrianov et al 1998, Bassett et al 2000, Bezerra et al 2004) Background inhomogeneous pseudoscalar (Kalb- Ramond) field (Majumdar and SenGupta, 1999) (Kar et al, 2001)

73. These proposals predict rotation of linear polarization independent of frequency Pseudoscalar-photon mixing in background magnetic field predicts rotation proportional to frequency The rotation required to explain the radio effect might conflict with the constraints from CMB B mode polarization

74. Alternatively the radio anisotropy might also arise due to intrinsic properties of radio galaxies in an anisotropic universe.

75. Large Scale Correlations of Optical Polarizations may be explained in terms of mixing of light with hypothetical pseudoscalars in background intergalactic magnetic field The intergalactic magnetic field is turbulent and has correlations over very large distance scales (Agarwal, Kamal and Jain, 2009)

76. Questions What constraints are imposed by CMB B modes on the different proposals? What do these proposals predict for the high z supernova data? Can these consistently explain all the different observations of anisotropy? Can we propose new techniques or observations to test for isotropy and to check the earlier claims?

77. Summary and Conclusions There appear to be many indications of violation of isotropy radio polarizations from radio galaxies optical polarizations from quasars CMB dipole, quadrupole and octopole with a preferred axis pointing towards Virgo We also find evidence for a dipole modulation of power and an anomalously cold spot in CMB

78. Summary and Conclusions Other data sets cluster peculiar velocities distribution of galaxies also indicate anisotropy

79. Summary and Conclusions Violation of isotropy persists even for high l CMB data Some of these effects may be simply due to residual foregrounds At high l, W band maps are found to be isotropic to a highly improbable degree. This may arise due to incorrect modeling of detector noise

80. Summary and Conclusions The physical cause of violation of isotropy is so far unknown

81. Thank You