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