Weighing neutrinos in the presence of a running primordial spectral index

The three-year WMAP(WMAP3), combined with other cosmological observations from galaxy clustering and Type Ia Supernova (SNIa), prefers a non-vanishing running of the primordial spectral index independent of the low CMB multipoles. Motivated by this feature we study cosmological constraint on the neutrino mass, which severely depends on what prior we adopt for the spectral shape of primordial fluctuations, taking possible running into account. As a result we find a more stringent constraint on the sum of the three neutrino masses, m_\nu < 0.76eV (2 \sigma), compared with m_\nu < 0.90eV (2 \sigma) for the case where power-law prior is adopted to the primordial spectral shape.