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 wi thin a hierarchical clustering scenario with a flat Gaussian initial pertur bation spectrum. The matching condition for fluctuation powers at the COBE scale and at the cluster scale leads to a strong upper limit on neutrino ma ss. For a flat universe with matter density parameter Omega = 0.3, we obtai n m(nu) < 0.6 eV for the Hubble constant H-0 < 80 km s(-1) Mpc(-1) Allowing for the more generous parameter space limited by Omega < 0.4, H-0 < 80 km s(-1) Mpc(-1) and age t(0) > 11.5 Gyr, the limit is 0.9 eV.