Limits on Neutrino Mass from Cosmic Structure Formation

We consider the effect of three species of neutrinos with nearly degenerate mass on the cosmic structure formation in a low-matter-density universe within a hierarchical clustering scenario with a flat Gaussian initial perturbation spectrum. The matching condition for fluctuation powers at the COBE scale and at the cluster scale leads to a strong upper limit on neutrino mass. For a flat universe with matter density parameter $\Omega =0.3\mathrm{}$, we obtain $m_{\nu }<0.6\mathrm{}\mathrm{eV}$ for the Hubble constant $H_0<80\mathrm{}\mathrm{km}{\mathrm{s}}^{-1\mathrm{}}{\mathrm{Mpc}}^{-1\mathrm{}}$. Allowing for the more generous parameter space limited by $\Omega <0.4,$ $H_0<80\mathrm{}\mathrm{km}{\mathrm{s}}^{-1\mathrm{}}{\mathrm{Mpc}}^{-1\mathrm{}}$ and age $t_0>11.5\mathrm{}\mathrm{Gyr}$, the limit is 0.9 eV.