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Cosmological signatures of primordial helical magnetic fields

Cosmological signatures of primordial helical magnetic fields. Tina Kahniashvili Carnegie Mellon University, USA Abastumani Astrophysical Observatory, Georgia Cosmological Magnetic Fields Monte Verita, Switzerland June 3 2009. Outline. General overview Space-time symmetry

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Cosmological signatures of primordial helical magnetic fields

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  1. Cosmological signatures of primordial helical magnetic fields Tina Kahniashvili Carnegie Mellon University, USA Abastumani Astrophysical Observatory, Georgia Cosmological Magnetic Fields Monte Verita, Switzerland June 3 2009

  2. Outline • General overview • Space-time symmetry • Parity symmetry violation - motivations • CMB fluctuations • Temperature anisotropies • Polarization • Polarized gravitational waves

  3. Cosmological Magnetic Field? • Observations: • Magnetic field in galaxies and clusters, 10-6-10-5 Gauss • Cosmic rays propagation 10-11 Gauss on 1 Mpc • Numerical simulations • Models (Kronberg’s talk) • Nonlinear process, magnetic field amplification, MHD • Cosmological magnetic field

  4. Some history… • E. Fermi “On the origin of the cosmic radiation”, PRD, 75, 1169 (1949) • F. Hoyle in Proc. “La structure et l’evolution de l’Universe” (1958) ” R. Beck, Scholarpedia article

  5. CMB vs. Magnetic Field • Magnetic field with an amplitude 10-8 -10-9 Gauss can leave “traces” on CMB Caprini, Finnelli, Kim, Kunze, Mattews, Paoletti talks

  6. The beauty of symmetry… • Spacetime in the Einstein model has no preferred or distinguishable direction; this proposition is known as • Lorentz invariance

  7. Why do we consider space-time symmetry breaking? • Theoretical models • Particle interactions in the standard model obey a number of symmetries: Under a parity transformation a system is replaced by its mirror image. In combination with charge conjugation, CP is a symmetry of the electromagnetic and chromodynamic interactions, while the electroweak interaction violates it. • Parity conservation or non-conservation is also relevant for cosmology, and may significantly affect the evolution of the universe. The excess of matter over antimatter is a result of CP-violation. • Several models beyond the Standard Model, such as string or quantum gravity theories lead to spontaneous violation of CPT symmetry.

  8. CPT SymmetryCosmological Context • In cosmological framework • CPT non-invariance can be viewed as providing a preferred direction in space-time • In the particle physics framework CPT violation is analogous to an external magnetic field Kostelecky 2008. • The early universe might serve as a ``laboratory" where cosmological observations can be used to test CPT symmetry. Lue, Wang, and Kamionkowski 1999 Feng et al. 2006 Cabella, Natoli, and Silk 2007, Xia et al. 2007, 2008

  9. Magnetic Helicity • Astrophysical Observations (Mirror symmetry breaking) • Sun magnetic field • Active galactic nuclei • Jets • How we observe magnetic helicity • The polarization of emitted synchrotron radiation T.A. Ensslin, 2003; J. P. Valee, 2004

  10. Magnetic Helicity Generation • Cosmological Sources Cornwall, 1997; Giovannini, 2000: Field and Carroll, 2000; Vachaspati 2001; Giovannini and Shaposhnikov 2001, Sigl 2002, Campanelli and Gianotti 2005, Semikoz and Sokoloff 2005, Campanelli, Cea and Tedesco 2008, Campanelli 2008 • MHD Processes in Astrophysical Plasma Vishniac and Cho, 2001; Brandenburg and Blackman, 2002; Subramanian, 2003; Vishniac, Lazarian and Cho, 2003; Subramanian and Brandenburg, 2004; Banerjee and Jedamzik, 2004, Subramanian 2007 • Turbulence Christensson, Hindmarsh, and Brandenburg, 2002; Verma and Ayyer, 2003, Boldyrev, Cattaneo and Rosner 2005;

  11. How could we measure magnetic helicity? • Direct test to probe magnetic fields (Faraday Rotation) DOES NOT APPLY to MAGNETIC HELICITY Ensslin and Vogt, 2003 Campanelli et al., 2004 Kosowsky et al., 2005 • Un-direct test (through induced specific effects) Difficult, BUT possible

  12. Why do we consider space-time symmetry breaking? • Observational Motivations • Astrophysics – can be explained by the late time generated helical magnetic fields • Cosmological observational puzzles • WMAP data –unexpected properties • Future missions, such PLANCK will provide us with more precise data and unable us to answer if do we need a crucial revision of the standard cosmological scenario. • Gravitational waves Astronomy – LISA

  13. Explanation? Extra-ordinary important to explain all un- expected observations under the same framework Most plausible will be to find out the physical well-motivated, natural reason (without addressing the speculative or/and unknown physics).

  14. Multipole coefficients North-South asymmetry “Cold” patch l=2, l=3, and l=5 (?) multipoles the same alignment Demianski & Doroshkevich 2007 Bernui 2008 Gao 2008 Cosmic Microwave Background Puzzles: Low Multipoles

  15. CMB anomalies – possible explanation • Preferred direction & Parity • Slightly anisotropic model • Cosmological defects • Symmetry breaking in the early Universe • Cosmological magnetic field • Others … unknown

  16. Cosmic Axis of Evil or Magnetic Field? Likehood: Kim and Naselsky 2009 Durrer, Kahniashvili, Yates, 1998 Chen, et ak, 2004 Kahniashvili, Lavrelashvili, Ratra, 2008

  17. CMB Non-Gaussianity • Can a magnetic field be a source?  T/T ~ B2 • Non-gaussianity in the source Brown and Crittenden 2005 CMB non-gaussianity? - Yes Seshadri and Subramanian 2009 Caprini et al. 2009

  18. Polarization Plane Rotation Angle: WMAPLorentz Symmetry or Parity Symmetry Violation? Komatsu et al. 2008

  19. Stochastic Magnetic Field Statistical Properties The parts of the magnetic field spectrum Normal MN(r) Ã FN(k); Longitudinal ML(r) Ã FN(k) Helical MH(r) Ã FH(k) The energy density E(r) Ã FN(k)

  20. Metric Perturbations from Magnetic field: helicity contribution • Scalar mode (density perturbations) – no contribution from magnetic helicity into the scalar part of the stress-energy tensor • Vector(vorticity perturbations, Alfven waves) Pogosian, Vachaspati, and Winitski, 2002, Kahniashvili and Ratra, 2005 Non-zero contribution ! CMB anisotropies • Tensor(gravitational waves) Caprini, Durrer, and Kahniashvili, 2004

  21. CMB temperature and polarization anisotropies • CMB temperature and polarization integral solutions of Boltzmann equation Hu and White 1997

  22. Radiation Field Stocks Parameters • I – intensity: ax2+ay2 • Q – polarization (linear) ax2-ay2 • U – polarization (linear) 2axay cos (x-y) • V – polarization (circular) 2axay sin(x-y) • I and V – invariants under rotation • Q ! U, U ! Q: Q2+U2 invariant

  23. Generation of Polarization anisotropy • Boltzmann equation • Scalar mode – only E-polarization • Propagation effects • Birefrigence • Lensing • Lorentz symmetry • Input: E –polarization • Output: B-polarization E and B polarization • E – electric: • North/South • East/West • B – magnetic • Northeast/Southwest • Northwest/Southeast

  24. CMB anisotropies parity even & odd power spectra • Parity-even power spectra: ClTT, ClEE, ClBB, ClTE • Helicity causes additional effects • Parity-odd power spectra: ClTB, ClEB • Vanishing in the standard model • Present if • Lorentz symmetry is broken • Homogeneous magnetic field • Parity symmetry is violated

  25. Parity Odd CMB fluctuations • An crucial test for the fundamental symmetry breakings. • It is more promising way to test primordial inflation or short-after inflation generated helicity. • This apply also for the Chern-Simons term induced parity symmetry violation (Lue, Wang, Kamionkowski 1999), but it has been shown that the signal is not observable through current or nearest future CMB missions

  26. Parity symmetry violation in the early Universe • Gravitational Chern-Simons term Lue, Wang, Kamionkowsky, 1999 Specific signatures on CMB – non-zero parity odd cross correlations between temperature & B-polarization; E & B-polarization anisotropies Lyth,Quimbay,Rodriguez 2005 Satoch, Kanno, Soda 2008 Saito, Ichiki, Taruya 2007 Seto, Taruya 2008

  27. Since Faraday rotation measurement is independent of magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM ! <|RM|2>1/2 Non-vanishing parity odd cross correlation between Temperature and B-polarization E- and B-polarization Parity Symmetry BreakingMagnetic Helicity How distinguish the source? Magnetic helicity or Lorentz symmetry violation?

  28. Additional TestsB-polarization peak position • Gravitational Waves • l ~ 100 (Polnarev 1985) • Lensing • l ~ 1000 (Seljak and Zaldarriaga 1996) • Magnetic field (primary effect – vector mode) • l ~ 2000 (Subramanian and Barrow 1998, Mack et al. 2002, Lewis 2004) • Magnetic field (secondary – faraday rotation • l ~15000 (Kosowsky et al. 2005)

  29. Lorentz Symmetry Violation • Analogy – an homogeneous magnetic field • Rotation angle / propagation distance • Cross correlations (off-diagonal) between TB and EB • Difference – frequency dependence • B-field / 1/2 • Lorentz symmetry violation /2 (in some models) • Can be frequency independent

  30. Maximal helicity effects • Significant reduction for parity-even power spectra (comparing with the non-helical case); • Comparable (by amplitude) cross correlations between temperature-E-polarization and temperature-B-polarization • Comparable (for large angular scales) cross correlations between temperature-E-polarization and E-B-polarization

  31. Vector mode Surviving up to small angular scales. Subramanian and Barrow, 1998; Lewis, 2004 Vanishing E-B polarization cross correlations (with respect of temperature-B- polarization). Kahniashvili and Ratra, 2005 Tensor mode Gravitational wave source damping after equality ! contribution in CMB for large angular scales (l <100) The same order of magnitude for temperature – B-polarization and E-B polarization cross correlations. Caprini, Durrer, and Kahniashvili, 2004 Vector – Tensor modes comparison

  32. CMB anisotropy parity odd power spectra (tensor mode) might reflect the presence of primordial magnetic helicity ClTB/ClTE (black); ClEB/ClEE (red) l=50, nS=-3 GWs sourced by a helical magnetic field B-polarization signal: the peak position insures to distinguish the source of the signal • Zaldariagga and Seljak, 1997 • Kamionkowsky, Kosowsky, & Stebbins, 1997 Caprini, Durrer, and Kahniashvili 2004

  33. How to constraint primordial magnetic helicity WARNING Even for a primordial magnetic field with maximal helicity such effects may be detectable if the current magnetic field amplitude is at least 10-9 Gauss on Mpc scales.

  34. Average helicity magnitude Measurement of temperature-B-polarization cross-correlations on small angular scales with Priors: • the magnetic field amplitude Kristainsen and Ferreira 2008, Giovannini and Kunze 2008 Finelli, Paci and Paoletti 2008 Yamazaki, Ichiki, Kajino and Mathews • the spectral indices ! average helicity constraint

  35. Magnetic Field LimitsKahniashvili, Samushia, Ratra 2009 Coming soon • Limits on cosmological magnetic field through WMAP 5 years BB-polarization signal assuming vector mode Kahniashvili, Maravin, Kosowsky 2009

  36. CMB Test • Apply only if the helical magnetic field is generated during inflation or short-after inflation (Garcia-Bellido talk) • Requires high enough magnitudes of the magnetic field itself • The amplitude of the magnetic field must be known from other tests

  37. Questions To Be Addressed • Magnetic helicity reflects the mirror symmetry violation • Does magnetic helicity explain North-South asymmetry? • Result in a preferred direction • Magnetic field – non-gaussianity • Most probably we can test presence of magnetic helicity through CMB non-gaussianity • Additional test to CMB parity odd cross correlations

  38. The averaged helicity spectrum amplitude HM(k,t) The averaged magnetic field energy spectrum amplitude EM(k,t) Schwatz’s inequality |HM(k,t)| · 2 EM(k,t)/k Total magnetic helicity HMtot (t) = s HM(k,t) dk Total magnetic energy density EMtot (t) = s EM(k,t) dk Correlation length- scale M(t)=s dk k-1 EM(k,t)/EMtot(t) HMtot (t) · 2 EMtot(t) M(t) The helical spectra

  39. Phase Transitions Magnetic Fields • If the generation process is causal • the maximal correlation length can not exceed the Hubble horizon H-1 at the moment of generation • QCD – 0.6pc, EWPT ~ 6 £ 10-4 pc • For  > max the magnetic field strength B/ Bmax(max/)+1/2 • E(k) ~ k for kmin<1/max • E(k) ~ k-5/3 – Kolmogoroff kmin<k<kD • Energy density arguments – EB (' B2max/8) · 0.1 rad Kahniashvili, Tevzadze, Ratra 2009 to be appear soon

  40. =2 white noise (Shafmann spectrum)or =4 (Batchelor spectrum) • Hogan 1983 -  =2 • Durrer and Caprini 2003  = 4 Caprini’s talk • In any case the amplitude of the magnetic field is too low to be detectable by CMB Davidson

  41. WARNING • The limits DO NOT APPLY to the inflation or re and pre-heating generated magnetic fields • Inflation generated magnetic fields n ~ -3 (scale invariant spectrum), Ratra 1992

  42. Magnetic Helicity can be tested through LISA • Polarized gravitational waves – manifestation of magnetic helicity Linearly polarized Circularly polarized

  43. Relic gravitational waves background From C. Hogan 2006

  44. GWs amplitude hc(f) vs. GWs energy density paramater G=GW/cr (where 2f=, cr=3H02/(8 G) Maggiore 2000: LISA Final Technical Report

  45. GWs from phase transitions Pioneering : Witten 1984, Hogan 1984 Earlier 90’s Turner & Wilczek, 1990 Kosowsky, Turner, & Watkins, 1992 Kamionkowski, Kosowsky, & Turner, 1994 • Bubbles collisions and nucleation • Turbulence • Hydro-turbulence • MHD (with and without helicity) • Kosowsky, Mack, Kahniashvili, 2002 • Dolgov, Grasso, Nicolis, 2002 • Nicolis 2002, • Kahniashvili, Gogoberidze, Ratra, 2005 • Caprini and Durrer, 2006…

  46. Main assumption on the turbulence model: Stationary developed case – Kolmogoroff’s hypothesis applies • Even accounting for inevitable decay – the emitted GWs spectrum will be close to that from stationary turbulence Justification: (Proudman 1975): If the turbulence is decaying additional terms proportional to time derivatives appear. But since the decay time d is at least several times larger than the turnover time, then the additional terms proportional to 1/d can be safely neglected Goldstein 1976 Analogy: acoustic waves generation by turbulence • Eddies length l0 and velocity v0 • Eddies characteristic frequency v0/l0 • Eddies characteristic wave-number 1/ l0 • Because v0 /c<1, the dark area is stretched along k axis. • GWs generating turbulent elements lie along k= line, so GW is given by eddy inverse turn-over time v0/l0 .

  47. k is normalized to 1 for k0 P(k) ~1 for helicity dominated turbulence nS=nH=-13/3 Polarization of GWs is observable by LISA, if the signal of GWs itself will be within the observation range Seto 2006 Degree of GWs circular polarization Kahniashvulu, Gogoberidze, and Ratra 2005

  48. Helical MHD inverse cascade turbulence Bishkamp & Muller 1999, Son 1999, Cristensoon, Hindmarsh, & Brandenburg 2003, Banerjee & Jedamzik 2004, Campanelli 2007 • Kinetic energy might be transferred to large scales (assuming helicity presence). Primordial magnetic field induces an additional GWs signal • The peak frequency of this secondary GWs is shifted at low frequency range • This allows to make GWs observable even if phase transitions occur at high energies • Another advantages • the maximal length scale is now comparable with Hubble horizon • the duration time of turbulence and correspondently the amplitude of the signal are changed

  49. Cristensoon, Hindmarsh, & Brandenburg 2003, Banerjee & Jedamzik 2004, Campanelli 2007 Inverse Cascade Models Time Evolution Eddy’s number 3

  50. Peak frequency fpeak=fH Peak amplitude GWs from MHD turbulence Kahniashvili, Gogoberidze, & Ratra, 2008

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