Cosmological signatures Cosmological signatures of of
primordial helical magnetic fieldsprimordial helical magnetic fields
Tina KahniashviliTina KahniashviliCarnegie Mellon University, USACarnegie Mellon University, USA
Abastumani Astrophysical Observatory, Georgia Abastumani Astrophysical Observatory, Georgia
Cosmological Magnetic FieldsCosmological Magnetic FieldsMonte Verita, SwitzerlandMonte Verita, Switzerland
June 3 2009June 3 2009
OutlineOutline
• General overview– Space-time symmetry
• Parity symmetry violation - motivations
• CMB fluctuations– Temperature anisotropies– Polarization
• Polarized gravitational waves
Cosmological Magnetic Field?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
Some history…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
CMB vs. Magnetic FieldCMB 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
The beauty of symmetry…The beauty of symmetry…• Spacetime in the Einstein model has no
preferred or distinguishable direction; this proposition is known as
• Lorentz invariance
Why do we consider Why do we consider space-time symmetry breaking?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.
CPT SymmetryCPT SymmetryCosmological ContextCosmological 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 1999Feng et al. 2006Cabella, Natoli, and Silk 2007,
Xia et al. 2007, 2008
Magnetic HelicityMagnetic 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
Magnetic Helicity GenerationMagnetic 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;
How could we measure magnetic helicity?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
Why do we consider Why do we consider space-time symmetry breaking?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
Explanation?Explanation?
Extra-ordinary important to explain all un-expected observations under the same framework
Most plausible will be to find out thephysical well-motivated, natural reason (without addressing the speculative or/and unknown physics).
Cosmic Microwave Background Cosmic Microwave Background Puzzles: Low MultipolesPuzzles: Low Multipoles
• 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
CMB anomalies – CMB anomalies – possible explanationpossible explanation
• Preferred direction & Parity – Slightly anisotropic model– Cosmological defects – Symmetry breaking in the early Universe– Cosmological magnetic field– Others … unknown
Cosmic Axis of Evil or Magnetic Field?Cosmic Axis of Evil or Magnetic Field?
Durrer, Kahniashvili, Yates, 1998
Chen, et ak, 2004
Kahniashvili, Lavrelashvili, Ratra, 2008
Likehood: Kim and Naselsky 2009
CMB Non-GaussianityCMB Non-Gaussianity
• Can a magnetic field be a source?
T/T ~ B2
• Non-gaussianity in the source
Brown and Crittenden 2005
CMB non-gaussianity? - YesSeshadri and Subramanian 2009
Caprini et al. 2009
Polarization Plane Rotation Angle: WMAPPolarization Plane Rotation Angle: WMAP
Lorentz Symmetry or Parity Symmetry Violation?Lorentz Symmetry or Parity Symmetry Violation?
Komatsu et al. 2008
Stochastic Magnetic Field Stochastic Magnetic Field Statistical PropertiesStatistical 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)
Metric Perturbations from Magnetic field: Metric Perturbations from Magnetic field: helicity contributionhelicity 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
CMB temperature and polarization CMB temperature and polarization anisotropiesanisotropies
• CMB temperature and polarization integral solutions of Boltzmann equation
Hu and White 1997
Radiation Field Radiation Field Stocks ParametersStocks Parameters
• I – intensity: ax2+ay
2
• Q – polarization (linear) ax2-ay
2
• 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
E and B polarizationE and B polarization
• E – electric: – North/South– East/West
• B – magnetic – Northeast/Southwest– Northwest/Southeast
• Generation of Polarization anisotropy – Boltzmann equation– Scalar mode – only E-
polarization
• Propagation effects– Birefrigence– Lensing– Lorentz symmetry
• Input: E –polarization
• Output: B-polarization
CMB anisotropies CMB anisotropies parity even & odd power spectra parity even & odd power spectra
• Parity-even power spectra:
ClTT, Cl
EE, ClBB, Cl
TE – Helicity causes additional effects
• Parity-odd power spectra:
ClTB, Cl
EB
– Vanishing in the standard model– Present if
• Lorentz symmetry is broken• Homogeneous magnetic field • Parity symmetry is violated
Parity Odd CMB fluctuationsParity 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
Parity symmetry violation in the early UniverseParity 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-polarizationanisotropies
Lyth,Quimbay,Rodriguez 2005Satoch, Kanno, Soda 2008Saito, Ichiki, Taruya 2007Seto, Taruya 2008
Parity Symmetry BreakingParity Symmetry BreakingMagnetic HelicityMagnetic Helicity
• 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
How distinguish the source?
Magnetic helicity or
Lorentz symmetry violation?
Additional TestsAdditional TestsB-polarization peak positionB-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)
Lorentz Symmetry ViolationLorentz 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
Maximal helicity effectsMaximal 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
Vector – Tensor modes comparisonVector – Tensor modes comparison
• 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
GWs sourced by a helical magnetic fieldGWs sourced by a helical magnetic field
CMB anisotropy parity odd power spectra (tensor mode) might reflect the presence of primordial magnetic helicity
ClTB/Cl
TE (black); ClEB/Cl
EE (red)
l=50, nS=-3
Caprini, Durrer, and Kahniashvili 2004
B-polarization signal: the peakposition insures to distinguishthe source of the signal• Zaldariagga and Seljak, 1997• Kamionkowsky, Kosowsky, & Stebbins, 1997
How to constraint primordial How to constraint primordial magnetic helicitymagnetic 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.
Average helicity magnitudeAverage helicity magnitude
Measurement of temperature-B-polarizationcross-correlations on small angular scales with
Priors: – the magnetic field amplitude
Kristainsen and Ferreira 2008, Giovannini and Kunze 2008
Finelli, Paci and Paoletti 2008Yamazaki, Ichiki, Kajino and Mathews
– the spectral indices
! average helicity constraint
Magnetic Field LimitsMagnetic Field Limits Kahniashvili, Samushia, Ratra 2009Kahniashvili, Samushia, Ratra 2009
Coming soon Coming soon• Limits on
cosmological magnetic field through WMAP 5 years BB-polarization signal assuming vector mode
Kahniashvili, Maravin, Kosowsky 2009Kahniashvili, Maravin, Kosowsky 2009
CMB TestCMB 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
Questions To Be AddressedQuestions 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
The helical spectraThe helical spectra
• 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 energydensity
EMtot (t) = s EM(k,t) dk
Correlation length-scale
M(t)=s dk k-1 EM(k,t)/EMtot(t)
HMtot (t) · 2 EM
tot(t) M(t)
Phase Transitions Magnetic FieldsPhase 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 / Bmax(max/)+1/2 – E(k) ~ k for kmin<1/max
– E(k) ~ k-5/3 – Kolmogoroff kmin<k<kD
• Energy density arguments – EB (' B2max/8) · 0.1 rad
Kahniashvili, Tevzadze, Ratra 2009to be appear soon
=2 white noise (Shafmann spectrum)=2 white noise (Shafmann spectrum)or or =4 (Batchelor spectrum) =4 (Batchelor spectrum)
• Hogan 1983 - =2• Durrer and Caprini
2003 = 4Caprini’s talk
• In any case the amplitude of the magnetic field is too low to be detectable by CMB
Davidson
WARNINGWARNING
• 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
Magnetic Helicity can be tested through Magnetic Helicity can be tested through LISALISA
• Polarized gravitational waves – manifestation of magnetic helicity
Linearly polarizedCircularly polarized
Relic gravitational waves backgroundRelic gravitational waves background
From C. Hogan 2006
GWs amplitude hGWs amplitude hcc(f) vs. GWs energy density paramater (f) vs. GWs energy density paramater
GG==GWGW//crcr (where 2 (where 2f=f=, , crcr=3H=3H0022/(8/(8 G) G)
Maggiore 2000:
LISA Final Technical Report
GWs from phase transitionsGWs 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…
• 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
Main assumption on the turbulence model: Main assumption on the turbulence model: Stationary developed case – Kolmogoroff’s hypothesis appliesStationary developed case – Kolmogoroff’s hypothesis applies
Goldstein 1976
Analogy: acoustic waves generation by turbulence 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 .
Degree of GWs circular polarization Degree of GWs circular polarization
• 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
Kahniashvulu, Gogoberidze, and Ratra 2005Kahniashvulu, Gogoberidze, and Ratra 2005
Helical MHD inverse cascade turbulenceHelical MHD inverse cascade turbulence
• 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
Bishkamp & Muller 1999, Son 1999,Cristensoon, Hindmarsh, & Brandenburg 2003, Banerjee & Jedamzik 2004, Campanelli 2007
Inverse Cascade Models Inverse Cascade Models Time EvolutionTime Evolution
• Cristensoon, Hindmarsh, & Brandenburg 2003,
• Banerjee & Jedamzik 2004, Campanelli 2007
Eddy’s number 3
GWs from MHD turbulenceGWs from MHD turbulence
• Peak frequency fpeak=fH
• Peak amplitude
Kahniashvili, Gogoberidze, & Ratra, 2008Kahniashvili, Gogoberidze, & Ratra, 2008
Turbulence Model IndependenceTurbulence Model Independence
• MHD turbulence induced GWs peak frequency is always associated with the Hubble frequency
Kahniashvili, Campanelli, Gogoberidze & Ratra 2008
GWs detectionGWs detection
EWPT Magnetic Field Induced EWPT Magnetic Field Induced GWsGWs
• VA2 ' 0.1
• VB ' 1/2Kahniashvili, Kisslinger, Stevens 2009
Another possibilityAnother possibilityCosmic rays particles arrival velocity correlatorCosmic rays particles arrival velocity correlator
Observable velocity correlator Kahniashvili & Vachaspati 2007
• Consider two known sources that are emitting charged particles that arrive on Earth.
• The particles would propagate along straight lines from sources to the Earth – if there is no magnetic field;
• The trajectories bent by the weak magnetic field;
ConclusionsConclusionsWhat We Are Looking ForWhat We Are Looking For
WMAP
PLANCKLISA
Atacama Space Telescope
Do We Need Cosmological Seed Do We Need Cosmological Seed Magnetic Fields?Magnetic Fields?
• Observed galaxies and cluster fields origin?
• Looks like we can explain them without addressing primordial relic seeds…
BUT
If the CMB un-expected featuresIf the CMB un-expected featureswill be confirmedwill be confirmed
• There is a good chance to explain them by natural reasons related to the relic magnetic field generation in the early Universe
If the relic gravitational waves background If the relic gravitational waves background will be detected by LISAwill be detected by LISA
and non-zero polarization will be seenand non-zero polarization will be seen
• Direct indication that the parity symmetry has been broken during the phase transitions
• It would be natural assume that parity symmetry violation consists on magnetic helicity
• Even if magnetic helicity has been generated earlier phase transitions, the input magnetic field will affect turbulence and will end up with MHD turbulence
CollaborationCollaboration• Leonardo Campanelli (INFN, Italy)• Chiara Caprini (Sacle, France)• Ruth Durrer (Geneva University, Swiss)• Grigol Gogoberidze (Abastumani Obs., Georgia)• Leonard Kisslinger (Carnegie Mellon University, USA)• Arthur Kosowsky (Pittsburgh University, USA)• George Lavrelashvili (Math Inst. Georgia)• Andrew Mack (Rutgers University, USA)• Yurii Maravin (Kansas State University, USA)• Trevor Stevens (Weslyan College, USA)• Bharat Ratra (Kansas State University, USA)• Alexander Tevzadze (Abastumani Obs., Georgia)• Tanmay Vachaspati (Case-Western Univ., USA)• Andrew Yates (Geneva University, Swiss)