1. Is there a preferred direction in the Universe P. Jain, IIT Kanpur There appear to be several indications of the existence of a preferred direction in the Universe (or a breakdown of isotropy)  Optical polarizations from distant AGNs  Radio polarizations from distant AGNs  Low order multipoles of CMBR

2. On distance scales of less than 100 Mpc the Universe is not homogeneous and isotropic The Virgo cluster sits at the center of this disc like structure Most galaxies in our vicinity lie in a plane (the supercluster plane) which is approximately perpendicular to the galactic plane. On larger distance scales the universe appears isotropic

3. CMBR What does CMBR fluctuations imply about the isotropy of the universe? CMBR is isotropic to a very good approximation

4. TT Cross Power Spectrum

5. The power is low at small l (quadrupole l=2) The probability for such a low quadrupole to occur by a random fluctuation is 5% Oliveira-Costa et al 2003 The Octopole is not small but very planar Surprisingly the Octopole and Quadrupole appear to be aligned with one another with the chance probability =1/62

6. Quadrupole Octopole Cleaned Map Oliveira-Costa et al 2003 All the hot and cold spots of the Quadrupole and Octopole lie in a plane, inclined at approx 30 o to galactic plane

7. Extraction of Preferred Axis Imagine  T as a wave function  Maximize the angular momentum dispersion  Oliveira-Costa et al 2003

8. Extraction of Preferred Axis k = 1 …3, m = -l … l Preferred frame e k  is obtained by Singular Value Decomposition e  represent 3 orthogonal axes in space The preferred axes is the one with largest eigenvalue   Ralston, Jain 2003 Alternatively Define

9. The preferred axis for both  Quadrupole and  Octopole points roughly in the direction (l,b)  (-110 o,60 o ) in Virgo Constellation

10. Hence WMAP data suggests the existence of a preferred direction (pointing towards Virgo) We (Ralston and Jain, 2003) show that there is considerable more evidence for this preferred direction  CMBR dipole  Anisotropy in radio polarizations from distant AGNs  Two point correlations in optical polarizations from AGNs Also point in this direction

11. CMBR Dipole The dipole is assumed to arise due to the local (peculiar) motion of the milky way, arising due to local in-homogeneities The observed dipole also points in the direction of Virgo

12. Physical Explanations Many explanations have been proposed for the anomalous behavior of the low order harmonics  Non trivial topology (Luminet, Weeks, Riazuelo, Leboucq and Uzan, 2003)  Anisotropic Universe due to background magnetic field (Berera, Buniy and Kephart, 2003)  Sunyaev Zeldovich effect due to local supercluster (Abramo and Sodre, 2003) A satisfactory explanation of the observations is still lacking

13.  Offset angle      RM)   RM : Faraday Rotation Measure   = IPA (Polarization at source) Anisotropy in Radio Polarizations  shows a Dipole ANISOTROPY Radio Polarizations from distant AGNs show a dipole anisotropy Birch 1982 Jain, Ralston, 1999 Jain, Sarala, 2003

15. Likelihood Analysis  The Anisotropy is significant at 1% in full (332 sources) data set and 0.06% after making a cut in RM (265 sources)  RM - | > 6 rad/m = 6 rad/m    = polarization offset angle

16. Distribution of RM The cut eliminates the data near the central peak

17. The radio dipole axis also points towards Virgo Jain and Ralston, 1999

18. Anisotropy in Extragalactic Radio Polarizations beta = polarization offset angle Using the cut |RM - | > 6 rad/m 2

19. Anisotropy in Extragalactic Radio Polarizations Using the cut |RM - | > 6 rad/m 2 Galactic Coordinates

20. Equatorial Coordinates Anisotropy in Extragalactic Radio Polarizations A generalized (RM dependent) statistic indicates that the entire data set shows dipole anisotropy

21. 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

22. Hutsemékers Effect Equatorial Coordinates 1<z<2.3

23. Statistical Analysis  A measure of alignment is obtained by comparing polarization angles in a local neighborhood The polarizations at different angular positions are compared by making a parallel transport along the great circle joining the two points

24. Maximizing d i (  ) with respect to  gives a measure of alignment D i and the mean angle Statistic  k, k=1…n v are the polarizations of the n v nearest neighbours of the source i  k  i = contribution due to parallel transport Statistic Jain, Narain and Sarala, 2003

25. We find a strong signal of redshift dependent alignment in a data sample of 213 quasars Alignment Results  Low polarization sample (p < 2%)  High redshift sample (z > 1) The strongest signal is seen in

26. Significance Level

28. Large redshifts (z > 1) show alignment over the entire sky

29. Alignment Statistic (z > 1)

30. Alignment Results Strongest correlation is seen at low polarizations ( p < 2%) at distance scales of order Gpc Large redshifts z > 1 show alignment over the entire sky Jain, Narain and Sarala, 2003

31. 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

32. Preferred Axis Optical axis is the eigenvector of S with maximum eigenvalue

33. Alignment Statistic Preferred axis points towards (or opposite) to Virgo Degree of Polarization < 2%

34. dipolequadoctoradiooptical dipole0.0200.0610.0420.024 quad0.0150.0230.004 octo0.0590.026 radio0.008 Prob. for pairwise coincidences Ralston and Jain, 2003

35. A satisfactory explanation of the observations is so far not available It is possible that the universe may not be isotropic even at cosmological scales. One should then explore generalization of the FRW metric the large scale anisotropies could arise due to : propagation in a large scale anisotropic medium The active galactic nuclei may be intrinsically correlated on very large distance scales. Similarly the CMBR quadrupole and octopole may be aligned at the source Physical Explanation

36. Alternatively the anisotropies could arise due to the local inhomogeneous distribution of matter This possibility cannot be ruled out for the CMBR and radio anisotropies but is unlikely to account for the large scale optical correlations, which is a redshift dependent effect Physical Explanation

37. The observations may also represent a fundamental violation of Lorentz invariance Lorentz invariance has been observed to be a very good symmetry of nature. Theoretically we expect that it is violated due to quantum gravity effects. We expect violations of order ( M Susy /M Planck ) 2 (Jain, Ralston 2005) Physical Explanation

38. We have been exploring the possibility that the effects may be explained by a light scalar (or pseudoscalar) Very light mass pseudoscalars (or scalars) are predicted by many theories beyond the Standard Model  Axion (Peccei-Quinn)  Supergravity  String theory A very light scalar or pseudoscalar may also be required to explain dark energy A common model for dark energy is a scalar field slowly rolling towards its true vacuum Light Scalars

39. Coupling to Photons Such a scalar field will have an effective coupling to photons It does not matter whether  is a scalar or a pseudoscalar If  is a scalar then this interaction breaks parity but parity is not a symmetry of nature.

40. This leads to reduced intensity of wave if the incident pseudoscalar flux is assumed negligible As the EM wave passes through large scale background magnetic field, photons (polarized parallel to transverse magnetic field) mix with pseudoscalars We are basically interested in electromagnetic waves propagating over astrophysical or cosmological distances in the presence of a background magnetic field.

41. This may also be partially responsible for dimming of distant supernovae (Csaki, Kaloper and Terning, 2002) The reduction in intensity due to pseudoscalar photon mixing in the local supercluster magnetic field may explain the anomalous CMBR quadrupole and octopole (Jain and Saha, work in progress)

42. The wave gets polarized perpendicular to the transverse magnetic field since only the component parallel to the background magnetic field mixes with pseudoscalars This may explain the optical alignment However we require magnetic field coherent on cosmologically large distance scales Polarization

43. Limit on the coupling For the invisible axion the current limit on the Peccei- Quinn symmetry breaking scale is 10 9 GeV, Mass < 0.01 eV (PDG) This particle gives very little contribution to mixing for galactic or intergalactic propagation. It may contribute in regions of strong magnetic fields and plasma density.

44. We are interested in a pseudoscalar whose mass may be much smaller g < 6 x 10 -11 /GeV (PDG) if we assume that the mass is negligible We will assume that its mass is smaller or comparable to the plasma density of the medium

45. Typical scales Background magnetic field for the case of Virgo supercluster is roughly 0.1  G, distance 1-10 Mpc Plasma density  10 -6 cm -3 For intergalactic propagation it may be reasonable to assume many domains of size 1 Mpc and B ≈ 0.005  G Plasma density  10 - 8 cm -3 We are interested in the frequency regime from radio to optical,  = 10 - 5 – 1 eV

46. Pseudoscalar Photon mixing We have considered this mixing in great detail so that it can be tested in future observations  Uniform background  Turbulent background ( Jain, Panda, Sarala, 2002 )  Slowly varying background (background magnetic field direction fixed) ( Das, Jain, Ralston, Saha, 2004 )  Slowly varying background with the direction of magnetic field varying with distance. (Das, Jain, Ralston, Saha, 2004)

47. Degree of Polarization as a function of l (or  ) Uniform Background

48. At source Q=0, U=0.4, V = 0.1 Stokes Parameters as a function of  (we set I = 1)

49. Degree of Polarization as a function of the distance of propagation The wave is unpolarized at source Resonant Mixing

50. Stokes parameter V as a function of Q for several different parameters (varying background magnetic field direction) V Q

51. A background pseudoscalar (scalar) field also leads to a rotation of the polarization of the wave Background pseudoscalar field Rotation in polarization =g  (    change in the pseudoscalar field along the path

52. Possible Explanation of Radio Anisotropy An anisotropically distributed background pseudoscalar field  of sufficiently large strength can explain the observations To account for the RM dependence Pseudoscalar field at source

53. Concluding Remarks There appears to be considerable evidence that there is a preferred direction in the Universe pointing towards Virgo However the CMBR observations may also be explained in terms of some local distortion of microwave photons due to supercluster. The physical mechanism responsible for this is not known so far. We are considering the possibility that it may be explained due to conversion of photons into pseudoscalars due to propagation through local supercluster magnetic field.

54. Concluding Remarks It is not possible to attribute optical alignment to a local effect since it is intrisically redshift dependent. We can explain this in terms of pseudoscalar photon mixing provided there exist magnetic fields coherent on cosmological distance scales Future observations will hopefully clarify the situation Radio anisotropy may also arise due to some local unknown effect. However it is difficult to find a physical mechanism which can accomplish this. An anisotropically distributed background pseudoscalar field may explain this effect.