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Cosmological signatures of primordial helical magnetic fields

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### 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
- Parity symmetry violation - motivations
- CMB fluctuations
- Temperature anisotropies
- Polarization
- Polarized gravitational waves

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…

- 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 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…

- Spacetime in the Einstein model has no preferred or distinguishable direction; this proposition is known as
- Lorentz invariance

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.

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

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

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;

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 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?

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).

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 MultipolesCMB anomalies – possible 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?

Likehood: Kim and Naselsky 2009

Durrer, Kahniashvili, Yates, 1998

Chen, et ak, 2004

Kahniashvili, Lavrelashvili, Ratra, 2008

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

Polarization Plane Rotation Angle: WMAPLorentz Symmetry or Parity Symmetry Violation?

Komatsu et al. 2008

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)

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

CMB temperature and polarization anisotropies

- CMB temperature and polarization integral solutions of Boltzmann equation

Hu and White 1997

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

Generation of Polarization anisotropy

- Boltzmann equation
- Scalar mode – only E-polarization
- Propagation effects
- Birefrigence
- Lensing
- Lorentz symmetry
- Input: E –polarization
- Output: B-polarization

- E – electric:
- North/South
- East/West
- B – magnetic
- Northeast/Southwest
- Northwest/Southeast

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

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

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

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 HelicityHow distinguish the source?

Magnetic helicity

or

Lorentz symmetry violation?

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)

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

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

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 comparisonCMB 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 fieldB-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

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.

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

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

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

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

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 spectraPhase 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
- Energy density arguments – EB (' B2max/8) · 0.1 rad

Kahniashvili, Tevzadze, Ratra 2009 to be appear soon

=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

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

Magnetic Helicity can be tested through LISA

- Polarized gravitational waves – manifestation of magnetic helicity

Linearly polarized

Circularly polarized

Relic gravitational waves background

From C. Hogan 2006

GWs amplitude hc(f) vs. GWs energy density paramater G=GW/cr (where 2f=, cr=3H02/(8 G)

Maggiore 2000:

LISA Final Technical Report

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…

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 .

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 polarizationKahniashvulu, Gogoberidze, and Ratra 2005

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

Cristensoon, Hindmarsh, & Brandenburg 2003,

Banerjee & Jedamzik 2004, Campanelli 2007

Inverse Cascade Models Time EvolutionEddy’s number 3

Peak frequency fpeak=fH

Peak amplitude

GWs from MHD turbulenceKahniashvili, Gogoberidze, & Ratra, 2008

Turbulence Model Independence

- MHD turbulence induced GWs peak frequency is always associated with the Hubble frequency

Kahniashvili, Campanelli, Gogoberidze & Ratra 2008

Another possibilityCosmic 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;

Do We Need Cosmological Seed 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 featureswill 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 will be detected by LISAand 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

Collaboration

- 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)

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