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_=_/₌, 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_, w, ₃₄) 1-A (k) ₃₄f_+B (k) f_^2-C (k) f_^3₌^ (z), where 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 integrated Sachs-Wolfe effect. We also modify the approximation of Eisenstein and Hu Astrophys. J. 511, 5 (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/nuₘatterₚower. f.