1. Constraints on the Primordial Magnetic Field and Neutrino Mass from the CMB Polarization and Power Spectra G. 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

2. Effects of a PMF Energy Density Lorentz force affects: Baryons & Electrons –Then Compton scattering affects photons Formation and evolution of LSS

3. 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

4. Power Spectral index n B : Characterize Stochastic Primordial Magnetic field = field strength smoothed on comoving scale = 1 Mpc Amplitude B :

5. Perturbed Einstein Equation

6. Boltzmann Equation Matter & Photon fluids { Lorentz force Compton scattering

7. Yamazaki, Ichiki, Kajino, Mathews (2008) Two-point Correlation Functions cut-off scale evolved from radiative viscosity

8. Vector and Tensor Modes Yamazaki, Ichiki, Kajino, Mathews PRD, 77 043005 (2008) Scalar Modes Two-point Correlation Functions Lorentz Force Energy

9. Vector Mode

10. Tensor Mode

11. A PMF affects both high and low multipoles Yamazaki, Ichiki, Kajino, Mathews PRD, 77, 043005 (2008) TT

12. Best Fit

13. MCMC likelihood functions vs. PMF parameters 88 H0H0 z reion Age

14. MCMC likelihood functions vs. PMF parameters bh2bh2 ch2ch2  nsns log(A s ) A t /A s B nBnB B = 0.4 nG n B = -1.9 – +1.6 -0.5 -2.0 +0.7

15. Constraints on Formation Epoch Yamazaki, Ichiki, Kajino, Mathews ApJ (2006) I.Inflation n B < -2.876 II.Electroweak n B < -2.43 III.Nucleosynthesis n B < -2.4 Caprini & Durrer (2002)

16. Effects of a Neutrino Mass Neutrino mass and B affect structure formation and  8 Kojima et al. PRD, 78, 045010 (2008) S V T

17. Effects of a Neutrino Mass Affects matter power spectrum differently than PMF

18. Constraint on the Neutrino Mass  m < 0.8 eV

19. Conclusions Best fit CMB: at a present scale of 1 Mpc. –B = 0.4 nG –< 2.02 (68% CL), < 2.85 ( 95% CL) nG –n B = -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