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)