COSMO 05
CMB Session
The Primordial Magnetic Field
and
The Cosmic Microwave Background
(Yamasaki etal, ApJL 625:L1=astro-ph/0410142 & astro-ph/0509xxx)
The University of Tokyo
&
National Astronomical
Observatory of Japan
D. G. Yamazaki ,
K . Ichiki , T. Kajino,
& G. Mathews
Background and Motivation
There is the gap between
observations and
theoretical calculations
for higher l
WMAP best fit cmbfast
For higher l, the temperature anisotropy of
CMB is not enough
cmbast : U. Seljak, et al., 1997, CBI: B. S. Mason et al., 2003,
WMAP: Bennett, et al., 2003, ACBAR: Kuo et al., 2004.
Introduction 1
For higher l, our understanding of the
temperature anisotropy of CMB is not
enough.
We need some new physical process for higher l.
Several semi-analytic studies point out that
the effect of the primordial magnetic field (PMF) is
very important in CMB for higher l.
(Jedamzik et al. 2000: Durrer et al. 2000, Mack et al. 2002 Subramanian and Barrow, 1998, 2002)
The PMF is one of the new physical process
for higher l
Those semi-analytic studies develop the CMB analysis.
Their approximations are appropriate for lower l, however ,
their accuracy is not enough to compare theoretical CMB
for higher l with observations.
We want to estimate the effect of the PMF on
CMB accurately, So we construct new
computation program which can calculate
scalar and vector mode effects of magnetic
fields on CMB.
Introduction 2
Another interesting subject
A cluster of galaxies have magnetic field of 0.1-1m (T. E.
Clarke et. al. 2000). But the origin and evolution of magnetic
field in the cluster of galaxies are not clearly understood.
The study of the PMF at the last scattering surface of
photons will provide important information to solve this
problem.
The attractive point of our study
We can solve these problems
simultaneously by studying the effect of the
PMF on the CMB.
Purpose
1. We construct a new computation program which can
calculate scalar and vector-mode effects of the PMF on CMB.
2. We estimate the PMF at 1Mpc by likelihood analysis with
the Markov Chain Monte Carlo (MCMC) method, in order to
solve the discrepancy between the theoretical primary CMB
and observational data (WMAP: Verde et al. 2003, ACBAR:
Kuo, C.L., et al., 2004, and CBI: Mason, B. S., et al., 2003)
for higher l.
3. We then discuss the evolution of the PMF.
Effect of PMF
All energy is the sum of the
Eall = EPMF + Efluid
PMF and the fluid
Lines of magnetic force
Lines of magnetic force
Lorentz force
MF
baryons
MF
Photon
Thomson scattering
Vector of photons is changed by
The Lorentz
force
changes
Thomson
scattering.
(photons
and
baryons
tight-coupled
before the
only are
vectors
of baryons
last scattering surface ).
magnetic
pressure
Repulsion between lines of
magnetic force
The magnetic field
increases the fluid pressure
Primordial Magnetic Field
We discard MHD back reaction onto the field itself within
the linear approximation ( Durrer et al., 2000).
We consider the primordial stochastic magnetic field. The
conductivity of the primordial plasma is very large, and it is
“frozen-in” (Mack et al. 2002). So, Electric field is neglected
E
0,
A time evolution of a magnetic field decouple from its spatial structure
on sufficiently large scales: Bl(τ, x)=Bl (x)/a2,
the power law: PB k  k nB
Our cosmological magnetic field model on the early universe is a
statistically homogeneous and isotropic random
 
Bl: magnetic comoving mean-field amplitude (at 1Mpc)
nB: power spectral index of the magnetic field
Our purpose is to constraint these two parameters.
Estimation of Primordial magnetic field strength
1. Combining Einstein equations with the fluid equations (Ma and
Bertschinger 1995, Hu and White 1997), we obtain evolution equations
of scalar and vector perturbations.
2. We evaluated the likelihood functions of WMAP, ACBAR, and CBI
data sets in a wide range of the magnetic field strength Bl and power
spectral index of the primordial magnetic field nB, with other
cosmological parameters, h, Wbh2, Wch2, ns,As, and t in flat Universe
models. To explore the parameter space, we make use of the Markov
chain technique (Lewis 2002).
3. We also take account of the SZ effect in our analysis. For that, we
follow an estimate of Komatsu and Seljak, with s8 = 0.9 (Spergel et at.
2003; Komatsu and Seljak 2002).
Result and Discussion I Numerical estimations
l(l+1)Cl [m K2]
B=8nG
B=6nG
The magnetic effect to
CMB perturbation
becomes strong for
higher l
500 1000 1500 2000 2500
l
For higher l, the effect of a primordial
magnetic field is much more important
Result and Discussion I Numerical estimations
WMAP+ACBAR+CBI :1 s (68%)
WMAP+ACBAR+CBI: 2 s 95%)
2s
1s
Excluded and allowed
regions at 1 and 2 s on
two parameter plane |Bl|
vs. nB , where |Bl| is the
primordial magnetic field
strength and nB is the
power-law spectral index.
The upper limit of the magnetic field strength
is |Bl| < 5.5 nG (1s)
The multiple constraints on generation scenario of PMF
WMAP+ACBAR+CBI :1 s (68%)
WMAP+ACBAR+CBI: 2 s 95%)
Lower limit from Cluster of galaxies
BBN
BBN limits on B
QCD
from the PMF
generation epoch inflation
①Our limit from WMAP + ACBAR +
CBI date sets
Bλ < 5.5 nG(1Mpc)
1
3
2
②Limit from the cluster of galaxies
Bλ > 1.0 nG
③Limit from gravity wave (Caprini
& Durrer 2002)
Allowed region of
the PMF from the
multiple constraints
categorized by the
generation epochs
inflation: 1
QCD: 1 + 2
BBN: 1 + 2 + 3
1.0 nG < Bl < 5.5 nG
-3.0 < nB < -2.3
Summary
1. We confirmed numerically (without approximation)
that potential discrepancy of CMB at higher l between
theory and observation is explained by the primordial
magnetic field.
2. Likelihood analysis of WMAP data with MCMC
method gives constraint on a primordial magnetic field,
B < 5.5nG
3. All constrains from the constraint of PMF by
gravity wave and recent magnetic field strength in
clusters of galaxies,
1 nG< B < 5.5 nG, -3.0 < nB < -2.3
in our estimated allowed parameter region.
Discussion
We considered only the isotropic collapse effect without
other evolutions of the PMF after the LSS (the last
scattering of photons).
If we include new effective evolution processes;
cluster merger → shock driven Weidel instability,
AGN origin of magnetic field,
the upper limit of the PMF may decrease from the present
estimate.
We should research others effective evolutions of the
cosmological primordial magnetic field after the last
scattering of photons.
Thank you very much for
your attention