Magnetic fields and CMB

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Eduardo Battaner, Estrella Florido, Ana Guijarro,
Africa Castillo Universidad de Granada
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• Reviews
• Grasso and Rubinstein (2001)
• Giovannini (2004)
• Distortion of Planck spectrum (Jedamzik,
  Katalinic and Olinto, 2000
• Faraday rotation (Kosowsky and Loeb, 1996)
• Shift in the position of Doppler peak (Adams,
  Danielson, Grasso and Rubinstein, 1996)
• Increase of amount of anisotropy (Giovannini,
  1999)
• Depolarization (Harari et al, 1997)

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Magnetogenesis

• B created
• After Recombination
• By turbulence in the radiation dominated epoch.
• In cosmological phase transitions.
• At Inflation. (assumed here)
• The radiation dominated era is highly
  resistive. Only large magnetic coherence cells
  can survive, mainly super-horizon cells.

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Pre-recombination magnetic fields

• 10-8-10-9 G (comoving) fields affect the
  formation of the large structure, introducing
  filaments at any large scale.
• AA papers
• Magnetic fields and large scale structure in a
  hot universe
• I. General equations
• II. Magnetic fields and filamentary structure.
• III. The polyhedric network.
• IV. The egg-carton universe.
• The fractal octohedron network of the large scale
  structure.
• Following these papers CMB must be affected by B,
  too.

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Radiation dominated era

• The mathematical procedure requires GR.
• Non-linear effects are not important. d is very
  small.
• From Annihilation to Equality.
• Energy-momentum tensor takes into account the
  magnetic contribution.
• This magnetic contribution acts anisotropically.
• ltBgt0, in agreement with the Cosmological
  Principle, but ltB2gt is not vanishing. It is
  ordered at coherence cells.

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Mean magnetic fields

• In the synchronous gauge

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...where

• Equation of state

Equation of state
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Perturbed quantities

• Probably the mean magnetic energy density is
  negligible in the Universe as a whole.
• Therefore, the expansion and the cooling rates of
  the Universe are unaffected by magnetic fields.
• However magnetic effects can be important at
  scales where isotropy does not hold.
• i.e. magnetic fields may play a role in producing
  the large scale of the Universe.
• Magnetic fields may play a role in CMB
  anisotropies and its interpretation.

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• The model does not include dark energy (yet)
• The model stops at Equality (transition between
  radiation and matter dominated eras).
• It is an step towards a future more detailed
  model.
• To follow a single structure (instead of
  considering a spectrum of primordial magnetic
  structures).

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linear perturbations
radiative
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EM quantities

• As the mean quantities vanish, perturbed
  quantities are

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Perturbed Equations

• Perturbations of general relativistic
• Maxwell equations
• Fluid equations of motion-energy
• Einstein field equations
• Not all equations are independent.

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Perturbed Maxwell equations
This reminds the frozen-in conditions, but rather
it shows that the magnetic pattern remains the
same. The strength is just reduced by the effect
of expansion. The original pattern is conserved!
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More Maxwell...
Macroscopic neutrality
Calculation of electrical current
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Perturbed equation of motion-energy

• From

i-component
Observe the Anisotropic action
0-component
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Perturbed Einstein Field Equation
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More field equations
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Energy density perturbations

• Let us define

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...some algebra

• Define present-day or comoving quantities

Probably, B0 does not coincide with B
at Present!
constant
It would coincide If only the expansion could
modify it
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...after miraculous algebra

• From 17 equations, we obtain for the density
  contrast

t is a time variable
Elliptic Linear Second order Differential eq.,
with Variables Coeff.
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Formation of CMB anisotropies

• Pre-existing magnetic configurations determine
  the evolution of radiation inhomogeneities.
• For very large t, i.e. for very large structures

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Primordial B

• If comoving magnetic strength is larger than
  about 0.01 microgauss, it should have had an
  important influence in CMB.
• If it is much larger the formation of galaxies
  would have begun too early and anisotropies in
  CMB would have been produced too early.
• If it is much lower, we meet the classical
  theory, without magnetic fields.
• If X is of order unity, we find equipartition,
  which is difficult to assume.

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Integration

• A primordial B configuration must be given as an
  input.
• The simplest configuration is a gaussian magnetic
  field flux tube

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General integration

• Simultaneous over-relaxation method with
  Chebyshev acceleration.
• As initial time condition we have considered
  either
• Homogeneity (d(t0)0)
• or
• Isocurvature (d(t0)-X)
• Except at the beginning, both provide similar
  results.

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Large scale tube fluxes

• In this case
• the integration is no longer elliptic,
• it can be treated analytically,
• more prediction ability.
• They are unaffected by dissipative effects.
• They are unaffected by resistive effects.
• They produce CMB anisotropies and density
  inhomogeneities unaffected by later non linear
  effects

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History

• Primordial magnetic flux tubes gives filamentary
  photon estructures. (DMbaryons)
• They are still observable at Recombination (CMB).
• Matter falls into the photon potential wells.
• After photon decoupling matter filamentary
  structures remain.

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...more history

• Large structures are unmodified by post
  Recombination non linear effects, damping...
• Small scale non-linear effects amplify and
  distort magnetic fields from B0 10-8 G to 10-6
  G observed today.
• No galactic dynamo amplification is required.

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Why filaments?

• They are natural coherence cells.
• They are found in many astrophysical systems.
• The large scale structure is rich in filaments.
• First example is Coma-A1367 supercluster.
• gt100 Mpc long, 10 Mpc in diameter.
• B has been measured in this supercluster (0.3-0.6
  mG in extracluster region)
• Is there a gt600 Mpc filament connecting Draco and
  Tucana?

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B and CMB

• B created at Inflation could have observable
  consequences in the last scattered surface.
• It could be difficult to identify filaments in
  maps.
• For instance, it would depend on the relative
  size and orientations of the structures in the
  LSS.
• But the interpretation of the power spectrum
  should be reconsidered. Also the polarization
  power spectrum.
• Filaments of magnetic origin with a component
  perpendicular to the LSS would produce FR. A
  correlation between FR and DT2 is therefore
  expected.

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Speculations

• Because of

Magnetic field lines either are straight lines
(in contradiction with the Cosmological
Principle) or form loops.
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And speculations...

• Assume there is a network of filaments.
• Many workers (Broadhurst, Tully, Einasto...)
  find that, even at scales larger than 100 Mpc.
• Tully A 3-dimension chess board
• Of course we are not proposing that the Universe
  is a pure crystal, but rather an imperfect
  network, like a foam lattice.
• The simplest network would consist in polyhedra.
• Assume that these filaments are fossil structures
  of previous magnetic field tubes.
• As a zero-order a crystalographic approach is not
  unreasonable.

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...and more speculations...

• Filaments arranged to form polyhedra defined by
  their edges.
• Edges are made of superclusters.
• Edges have formed by primordial magnetic tubes.
  Then, the edges have a direction and form
  loops.
• What is the basic polyhedra of the lattice?

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...Following speculations...

• Magnetism imposes restrictions on the basic
  polyhedra.
• If all edges, all vertexes and faces are
  equivalent.
• Nature cannot solve puzzles
• The loops must close in a face. This is the
  simplest.
• The basic polyhedron must be the octahedron.

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The egg-carton Universe

• Octahedra contacting at their vertexes.
• Other possibilities are too complicated.

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A model Universe
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Identification

• Most important superclusters reasonably fit the
  egg-carton lattice.
• Most voids fit this lattice too.
• There would be two kinds of voids intra- and
  inter-octahedra.

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If magnetic energy density is negligible

• As always, however...

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For a Robertson-Walker metric
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