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Constraints on the Primordial Magnetic Field and Neutrino Mass from the CMB Polarization
and Power SpectraG. J. Mathews - University of Notre Dame
D. . Yamazaki, T. Kajino, NAOJ
K. Ichiki, Nagoya Univ.
International Conference on Cosmological Magnetic Fields Monte Verità, Ascona, Switzerland
May 31-Jine 5, 2009
Yamazaki, Ichiki, Kajino, Mathews, Submitted (2009), Yamazaki et al 2008; Kojima et al. 2008
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Effects of a PMF
• Energy Density
• Lorentz force affects: Baryons & Electrons
– Then Compton scattering affects photons
• Formation and evolution of LSS
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Cosmic Structure Effects 8 “alternative normalization parameter”
RMS matter density fluctuation in co-moving sphere of radius 8h-1 Mpc
• Observations give 0.7 < 8 < 0.9– (Tegmark et al 2006; Cole et al. 2005; Rozo et al.
2007; Ross et al. 2008) 8 affects CMB (e.g. SZ effect)• B affects 8 and CMB m affects 8 and CMB
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Power Spectral
index nB :
Characterize Stochastic Primordial Magnetic field
= field strength smoothed on comoving scale = 1 Mpc
Amplitude B :
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Perturbed Einstein Equation
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Boltzmann Equation
Matter& Photon fluids {
Lorentz force
Compton scattering
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Yamazaki, Ichiki, Kajino, Mathews (2008)
Two-point Correlation Functions
cut-off scale evolved from radiative viscosity
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Vector and Tensor Modes
Yamazaki, Ichiki, Kajino, Mathews PRD, 77 043005 (2008)
Scalar Modes
Two-point Correlation Functions
Lorentz Force
Energy
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Vector Mode
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Tensor Mode
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A PMF
affects both high and
low multipoles
Yamazaki, Ichiki, Kajino, Mathews PRD, 77, 043005 (2008)
TT
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Best Fit
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MCMC likelihood functions vs. PMF parameters
8
H0
zreion
Age
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MCMC
likelihood functions vs. PMF parameters
bh2
ch2
ns
log(As)
At/As
B nB
B = 0.4 nG
nB = -1.9
–
+1.6-0.5
-2.0+0.7
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Constraints on Formation Epoch
Yamazaki, Ichiki, Kajino, Mathews ApJ (2006)
I. Inflation nB < -2.876
II. Electroweak nB < -2.43
III. Nucleosynthesis nB < -2.4
Caprini & Durrer (2002)
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Effects of a Neutrino MassNeutrino mass and B affect structure formation and 8
Kojima et al. PRD, 78, 045010 (2008)
SV
T
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Effects of a Neutrino Mass
Affects matter power spectrum differently than PMF
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Constraint on the Neutrino Mass
m< 0.8 eV
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Conclusions
• Best fit CMB: at a present scale of 1 Mpc.– B = 0.4 nG
– < 2.02 (68% CL), < 2.85 ( 95% CL) nG
– nB = -1.9
– < -1.18 ( 68% CL), < -0.46 ( 95% CL)
– Neutrino masses m< 0.8 eV (N= 3).
• Possibility exists to confirm existence of a PMF
• Could constrain formation epoch
+0.7-2.0
+1.6-0.5
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