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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

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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
Outline

  • 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 field
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
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
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 symmetry cosmological context
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
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
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
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 breaking1
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
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).


Cosmic microwave background puzzles 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

Cosmic Microwave Background Puzzles: Low Multipoles


Cmb anomalies possible explanation
CMB 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
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
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 wmap lorentz symmetry or parity symmetry violation
Polarization Plane Rotation Angle: WMAPLorentz Symmetry or Parity Symmetry Violation?

Komatsu et al. 2008


Stochastic magnetic field statistical properties
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
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 anisotropies contribution

  • CMB temperature and polarization integral solutions of Boltzmann equation

    Hu and White 1997


Radiation field stocks parameters
Radiation Field contributionStocks 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


E and b polarization

  • Generation of Polarization anisotropy contribution

    • 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


Cmb anisotropies parity even odd power spectra
CMB anisotropies contributionparity 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
Parity Odd CMB fluctuations contribution

  • 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
Parity symmetry violation in the early Universe contribution

  • 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


Parity symmetry breaking magnetic 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

Parity Symmetry BreakingMagnetic Helicity

How distinguish the source?

Magnetic helicity

or

Lorentz symmetry violation?


Additional tests b polarization peak position
Additional Tests magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM B-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
Lorentz Symmetry Violation magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM

  • 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
Maximal helicity effects magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM

  • 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 comparison

Vector mode magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM

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


Gws sourced by a helical magnetic field

CMB anisotropy parity odd magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM

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


How to constraint primordial magnetic helicity
How to constraint primordial magnetic helicity magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM

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
Average helicity magnitude magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM

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 limits kahniashvili samushia ratra 2009 coming soon
Magnetic Field Limits magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM Kahniashvili, 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
CMB Test magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM

  • 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
Questions To Be Addressed magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM

  • 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 spectra

The averaged helicity spectrum amplitude H magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM M(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


Phase transitions magnetic fields
Phase Transitions Magnetic Fields magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM

  • 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


2 white noise shafmann spectrum or 4 batchelor spectrum
magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM =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
WARNING magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM

  • 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
Magnetic Helicity can be tested through LISA magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM

  • Polarized gravitational waves – manifestation of magnetic helicity

Linearly polarized

Circularly polarized


Relic gravitational waves background
Relic gravitational waves background magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM

From C. Hogan 2006


Gws amplitude h c f vs gws energy density paramater g gw cr where 2 f cr 3h 0 2 8 g
GWs amplitude h magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM c(f) vs. GWs energy density paramater G=GW/cr (where 2f=, cr=3H02/(8 G)

Maggiore 2000:

LISA Final Technical Report


Gws from phase transitions
GWs from phase transitions magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM

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: magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM 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 .


Degree of gws circular polarization

k is normalized to 1 for k magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM 0

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


Helical MHD inverse cascade turbulence magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM

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


Inverse cascade models time evolution

Cristensoon, Hindmarsh, & Brandenburg 2003, magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM

Banerjee & Jedamzik 2004, Campanelli 2007

Inverse Cascade Models Time Evolution

Eddy’s number 3


Gws from mhd turbulence

Peak frequency f magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM peak=fH

Peak amplitude

GWs from MHD turbulence

Kahniashvili, Gogoberidze, & Ratra, 2008


Turbulence model independence
Turbulence Model Independence magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM

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

    Kahniashvili, Campanelli, Gogoberidze & Ratra 2008


Gws detection
GWs detection magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM


Ewpt magnetic field induced gws

V magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM A2' 0.1

VB' 1/2

EWPT Magnetic Field Induced GWs

  • Kahniashvili, Kisslinger, Stevens 2009


Another possibility cosmic rays particles arrival velocity correlator
Another possibility magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM Cosmic 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;


Conclusions

Conclusions magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM

WMAP

What We Are Looking For

Atacama Space

Telescope

LISA

PLANCK


Do we need cosmological seed magnetic fields
Do We Need Cosmological Seed Magnetic Fields? magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM

  • Observed galaxies and cluster fields origin?

  • Looks like we can explain them without addressing primordial relic seeds…

    BUT


If the cmb un expected features will be confirmed
If the CMB un-expected features magnetic helicity, the amplitude and configuration of a primordial magnetic field could be obtained through CMB polarization plane RM will 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
Collaboration by LISA

  • 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)


Thanks by LISA


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