Primordial Generation of Magnetic Fields

Primordial Generation of Magnetic Fields

Arun Kumar PandeyPhysical Research Laboratory

Ahmedabad

DAE-BRNS Symposium(DEC 10, 2014)

Today’s Observational status

Today:

Observed at all scales.

z 20-15≳

10 z≳

Today’s Observational status

Today:

Observed at all scales.

z 20-15≳

10 z≳

Today’s Observational status

Today:

Observed at all scales.

z 20-15≳

10 z≳

Today’s Observational status

Today:

Observed at all scales.

z 20-15≳

10 z≳

Today’s Observational status

Today:

Observed at all scales.

WHAT IS THE ORIGIN OF THESE MAGNETIC FIELDS ?

z 20-15≳

10 z≳

Limits

Cosmological Generation: Inflation B ≈ 10^(-34) -10^(-9) G [At Mpc scale], [Turner & Widrow 1988]

Phase transitions in the early Universe: B ≈ 10^(-20) G [QCD phase transition, at 10 Mpc scale]

[Sigl et al. 1997]

Astrophysical Generation: Battery processes: B ≈ 10^(-18) G [Biermann battery, kpc scale] [Xu et al. 2008

Plasma fluctuations: B ≈ 10^(-16) G [IGM after reionization] [Schlickeiser 2012]

Two Possibilities for the origin: and difficulties

FIRST ONE :Generation during the structure formation

Astrophysical origin

Astrophysical origin only explains the origin and amplifications of the magnetic fields up to a length scale of few kpc.

Two Possibilities for the origin: and difficulties

SECOND ONE:Generated in the Primordial universe.

Primordial Origin have no difficulty in accounting for the length scale.

Primordial origin

Problem with these two possibilities

Both recent and primordial

generation mechanisms have difficulties in

explaining theobservations.

Astrophysical mechanisms

fails to explain fields at cosmological scale.

Seed fields are too weak!

Origin of Magnetic Fields

We are interested only in generation of magnetic fields on very large scale (~ Mpc), so we will discuss only primordial origin (as these mechanism have no difficulty in accounting for

the length of coherence.)

Generation of Magnetic Seed Fields

Amplification of Seed Fields by Small-Scale Dynamo

Primordial Origin

Generation and Evolution

● We applied a kinetic theory with some quantum field theory inspired corrections to the EW plasma, to incorporate parity odd physics.

● Recently Son and yamamoto [ Phys. Rev. D 87, 8, 085016 (2013)] has shown that, by modifying the kinetic equations by taking into account the Berry curvature flux, these parity violating term comes automatically.

By applying this, we have found that the parity violating term coming from the effect of Berry correction, generate asymmetry between the particles and antiparticles number density, in the EW plasma. Which leads to a very large magnetic field before EW scale at a very large length scale.

Generation and Evolution

● Modification of the Kinetic equation

(1)

● Now total current do not conserved because of

(2)

where

● Using Maxwell's equations, we can get evolution equation for magnetic field as

Let Bz = 0. In that case

● So we have instability for k <β and k < σ / or k > β and k > σ / . So unstable modes will ∝ ∝grow exponentially.

Generation and Evolution

Where

● So number of right electrons varies with Chern Simons number as

Where and

Using these two, we have estimated the field strength. We have found that magnetic field a

field strength of B 〜 10^(23) G at a length scale of 〜 10^(3) /GeV. [A.P, J. Bhatt 2014 (under preparation)]

Generation and Evolution

So we have found that, with the consistent kinetic theory with Berry correction, magnetic field of large magnitude can be generated at very large length scale, before EW scale.

Thank You

Supplementary Slides

Observational Tools

● Zeeman effect (B||; atomic and molecular gas)● Faraday rotation (B||); ionized gas)● Radio continuum polarization (B⊥; relativistic electrons)● Polarization from aligned dust grains (B⊥ orientation only; dense gas and dust)

B|| means along the line of sight; B⊥ means in the plane of the sky.

.Third way to generate magnetic field

In addition to the astrophysical and cosmological mechanisms, there is a third category for the generation of large-scale magnetic fields. Small density fluctuations during the cosmological recombination of hydrogen atoms inevitably induce magnetic fields. Compton and Coulomb scatterings are so efficient that photons, protons,and electrons are approximated to a tightly coupled fluid. If these three kinds of fluidsmoved in exactly the same way, magnetic fields could not be generated. However, because photons scatter off electrons preferentially, compared with protons, small differences in velocity between protons and electrons are generated, which yields an electric current.

Cosmological Magnetic Field: A Fossil of Density Perturbations in the Early Universe Kiyotomo Ichiki et al. Science 311, 827 (2006); DOI: 10.1126/science.1120690

Primordial Origin● Cosmological defects

❖ Phys. Rev. Lett. 67, 1057 (1991).❖ Phys. Rev. D 56, 3238 (1997)❖ Phys. Rev. D 56, 3238 (1997)

● Phase transitions ❖ Phys.Lett. B265, 258261, 1991.

● Inflation ❖ Phys. Rev. D 37 (1988) 2743.❖ Phys. Rev. D 41 (1990) 1231.❖ Phys. Rev. D 62, 103512 (2000)

● Electroweak anomaly❖ Phys. Rev. D 56,6146 (1997)

● String cosmology❖ Phys. Rev. Lett. 75, 3796 (1995)

● Temporary electric charge nonconservation❖ Phys. Rev. D 47, 3144 (1993).

● Trace anomaly❖ Phys. Rev. D 48, 2499 (1993)

● Breaking gauge invariance❖ Phys. Rev. D 37 (1988) 2743.

Primordial Origin have no difficulty in accounting for the length of coherence.

Astrophysical origin

● Top-Down (10-20 kpc)● Bottom-Up

(from few pc to 5 kpc)

Top Down Bottom Up