Constraints on the Primordial Magnetic Field and Neutrino Mass from the CMB Polarization and Power...
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Transcript of Constraints on the Primordial Magnetic Field and Neutrino Mass from the CMB Polarization and Power...
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
Effects of a PMF
• Energy Density
• Lorentz force affects: Baryons & Electrons
– Then Compton scattering affects photons
• Formation and evolution of LSS
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
Power Spectral
index nB :
Characterize Stochastic Primordial Magnetic field
= field strength smoothed on comoving scale = 1 Mpc
Amplitude B :
Perturbed Einstein Equation
Boltzmann Equation
Matter& Photon fluids {
Lorentz force
Compton scattering
Yamazaki, Ichiki, Kajino, Mathews (2008)
Two-point Correlation Functions
cut-off scale evolved from radiative viscosity
Vector and Tensor Modes
Yamazaki, Ichiki, Kajino, Mathews PRD, 77 043005 (2008)
Scalar Modes
Two-point Correlation Functions
Lorentz Force
Energy
Vector Mode
Tensor Mode
A PMF
affects both high and
low multipoles
Yamazaki, Ichiki, Kajino, Mathews PRD, 77, 043005 (2008)
TT
Best Fit
MCMC likelihood functions vs. PMF parameters
8
H0
zreion
Age
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
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)
Effects of a Neutrino MassNeutrino mass and B affect structure formation and 8
Kojima et al. PRD, 78, 045010 (2008)
SV
T
Effects of a Neutrino Mass
Affects matter power spectrum differently than PMF
Constraint on the Neutrino Mass
m< 0.8 eV
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