Neutrino Mass, Dark Energy, and the Linear Growth Factor

We study the degeneracies between neutrino mass and dark energy as they manifest themselves in cosmological observations. In contradiction to a popular formula in the literature, the suppression of the matter power spectrum caused by massive neutrinos is not just a function of the ratio of neutrino to total mass densities f_nu=Omega_nu/Omega_m, but also each of the densities independently. We also present a fitting formula for the logarithmic growth factor of perturbations in a flat universe, f(z, k;f_nu,w,Omega_DE)= (1-A(k)*Omega_DE*f_nu+B(k)*f_nu^2-C(k)*f_nu^3)*Omega_m(z)^alpha, where alpha depends on the dark energy equation of state parameter w. We then discuss cosmological probes where the f factor directly appears: peculiar velocities, redshift distortion and the Intergrated Sachs-Wolfe effect. We also modify the approximation of Eisenstein & Hu (1999) for the power spectrum of fluctuations in the presence of massive neutrinos and provide a revised code (http://www.star.ucl.ac.uk/~lahav/nu_matter_power.f)