Neutrino Perturbations in CMB Anisotropy and Matter Clustering

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  • 29 October 2003
Abstract
We present a detailed analytical study of ultra-relativistic neutrinos in cosmological perturbation theory and of the observable signatures of neutrino perturbations. By modifying perturbation variables, we eliminate all the time derivatives of scalar gravitational potentials from the dynamical equations. This notably simplifies the equations and their solutions. Our density perturbation variables are generally constant on superhorizon scales. In real space the analytical approach can be extended beyond fluid models and applied to neutrinos. We find that neutrino perturbations suppress the acoustic peaks in the cosmic microwave background (CMB) for the multipoles with l>200 but enhance the amplitude of matter fluctuations on these scales. In addition, they generate a *unique phase shift* in the CMB acoustic oscillations that, for adiabatic modes, cannot be produced by any other standard physics. The origin of the phase shift can be traced to neutrinos propagating faster than the sound speed of the photon-baryon plasma. We also show that the low l integrated Sachs-Wolfe effect is not sensitive to neutrinos. The faster cosmological expansion due to the energy of the neutrino background changes the CMB acoustic and damping scales, but equivalent changes can be produced by varying other standard parameters, including the primordial helium abundance. We find that from a high resolution, low noise instrument such as CMBPOL the effective number of light neutrino species can be determined with an accuracy of sigma(N_nu) = 0.05 to 0.09, depending on the constraints on the helium abundance.

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