Understanding the CMB Neutrino Isocurvature modes S. MUYA KASANDA School of Mathematical Sciences University of KwaZulu-Natal Supervisor: Dr K. Moodley SA SKA Postgraduate Conference December 2008

CMB & Initial conditions Measurements of CMB anisotropies: - provide us with important information about the formation of LSS, - give insights into the initial conditions Adiabatic I.C. Isocurvature I.C: - Cold Dark Matter Isocurvature - Neutrino Density Isocurvature (NID) - Neutrino Velocity Isocurvature (NIV) - Baryon Isocurvature

Perturbation equations & Initial conditions Adiabatic I.C. Isocurvature I.C. - Cold Dark Matter Isocurvature - Neutrino Density Isocurvature (NID) - Neutrino Velocity Isocurvature (NIV) - Baryon Isocurvature Previous works have shown a possible contribution from Neutrino Isocurvature modes to the CMB power spectrum up to 40% (Dunkley et al, 2006; Bucher et al, 2000; Moodley et al, 2004). We investigate the signatures and features of Neutrino Isocurvature initial conditions in the CMB power spectrum.

Methodology Derive accurate analytical expressions for the photon density perturbations, the photon shear, the baryon velocity divergence and the gravitation potential for NID and NIV modes Project the perturbations, evaluated at the last scattering surface to find the spectrum of anisotropies today. Compute the CMB angular power spectrum in NID and NIV models Study the impact of cosmological parameters on the CMB angular power spectrum in NI models.

Analytical expressions for the perturbations NIVNID where

… for NID

… for NIV

CMB angular power spectrum It tells us about the power of temperature anisotropies on angular scale approx. 180/l

Impact of the baryon density on the CMB power spectrum

Neutrino Isocurvature Polarization where Photon shear

Neutrino Isocurvature Polarization on large scale l(l+1)Cl prop. l^4 for Adiab l^4 for NID l^2 for NIV

Some important points so far… The amplitude of the acoustic oscillations is proportional to – 1/(1+R) 1/2 for NID mode – 1/(1+R) for NIV mode In NID mode, the main contribution to the CMB anisotropies comes from the photon density contrast on all scales. In NIV mode, photon-baryon velocity contribution dominates on large scale, gravitational potential contribution dominates on small scales The frequency of the acoustic oscillations (or, the effective sound speed) is approximately the same in NID mode than in NIV mode, but greater than an adiabatic mode. In NI modes, as the baryon density increases, the peaks of the spectrum shift slightly to higher l, and the whole spectrum is lowered. This effect of lowering the peaks is stronger in NIV models than in NID models. The CMB polarization power spectrum (on large scales) is proportional to ℓ^4, ℓ^4 and ℓ^2 for the adiabatic, the neutrino isocurvature density and the neutrino isocurvature velocity modes respectively. These features can be used to constrain the neutrino isocurvature velocity mode.

Way forward… Investigate the secondary anisotropies for the NID and NIV modes.

Thank you.

From perturbation equations to CMB power spectrum Source function Multipole moments (Transfer function) CMB Power spectrum densitiesvelocitiesMetric fields