Neutrino mass, dark energy, and the linear growth factor
Angeliki Kiakotou, { \ O} ystein Elgar{\o}y, and Ofer Lahav

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, $f(z, k;f_\nu,w,\Omega_{\rm DE}) \approx [1-A(k)\Omega_{DE}f_{\nu}+B(k)f_{\nu}^{2}-C(k)f_{\nu}^{3}] \Omega_{m}^{\alpha}(z)$, 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 (1998) for the power spectrum of fluctuations in the presence of massive neutrinos and provide a revised code\footnote {http://zuserver2.star.ucl.ac.uk/$\sim$lahav/nu\_matter\_power.f}.

© 2008 The American Physical Society.