Cosmological limit on the neutrino mass

We perform a careful analysis of constraints on the neutrino mass from current cosmological data. Combining data from the cosmic microwave background and the 2dF galaxy survey yields an upper limit on the sum of the three neutrino mass eigenstates of $\sum m_{\nu }<~3\mathrm{eV}$ (95% C.L.), without including additional priors. Including data from SNIa observations, big bang nucleosynthesis, and HST Hubble key project data on $H_0$ tightens the limit to $\sum m_{\nu }<~2.5\mathrm{eV}$ (95% C.L.). We also perform a Fisher matrix analysis which illustrates the cosmological parameter degeneracies affecting the determination of $\sum m_{\nu }.$