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