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, mν < 0.76eV (2 σ), compared with mν < 0.90eV (2 σ) for the case where power-law prior is adopted to the primordial spectral shape.
PACS number(s): 98.80.CqThe three year Wilkinson Microwave Anisotropy Probe observations (WMAP3) [1,2,3,4, 5] have marked another milestone on the precision cosmology of the Cosmic Microwave Background (CMB) Radiation. The simplest six-parameter power-law ΛCDM cosmology is in remarkable agreement with WMAP3 together with the large scale structure(LSS) of galaxy clustering as measured by 2dF [6] and SDSS [7] and with the Type Ia Supernova (SNIa) as measured by the Riess "gold" sample [8] and the first year SNLS [9]. This agreement between the above "canonical" cosmological model and observations can be used to test a number of possible new physics, such as the equation of state of dark energy, neutrino masses, time variation of fundamental constants, etc.Among them, the constraint on the neutrino or hot dark matter mass can be obtained from the freestreaming modification of the transfer function of the matter power spectrum. We should note, however, that if one allowed any shape of primordial spectrum, the freestreaming effect could easily be compensated by some nontrivial shape of the primordial spectrum, so that one cannot obtain sensible limit on the neutrino mass. That is, we can obtain a nontrivial bound on neutrino mass if and only if we adopt some prior on the shape of primordial power spectrum such as a simple power-law. From the above argument, we expect that as we allow more degrees of freedom on the primordial spectrum beyond a power-law, the constraint on the neutrino mass would be less stringent in general.As for the shape of the primordial power spectrum, it is noteworthy that a significant deviation has been observed by WMAP3 from the simplest Harrison-Zel'dovich spectrum, and that this feature is more eminent with the combination of all the currently available CMB, LSS and SNIa (dubbed the case of "All" in [5]). Moreover, a nontrivial negative running of the scalar spectral index α s , whose existence was studied even before WMAP epoch [10,11], was favored by the first-year WMAP papers [12,13,14]. But its preference was somehow diminished as corrections to the likelihood functions were made [15].However, the new WMAP3 data prefers again a negative running in the "All" combination [5].If confirmed, a nonvanishing running of α s would not only constrain inflationary cosmology significantly [16,17,18,19,20,21], but also affect the cosmological c...