Impact of assuming flatness in the determination of neutrino properties from cosmological data

Cosmological data have provided new constraints on the number of neutrino species and the neutrino mass. However, these constraints depend on assumptions related to the underlying cosmology. Since a correlation is expected between the number of effective neutrinos N-eff, the neutrino mass Sigma m(v), and the curvature of the universe Omega(k), it is useful to investigate the current constraints in the framework of a nonflat universe. In this paper we update the constraints on neutrino parameters by making use of the latest cosmic microwave background data from the Atacama Cosmology Telescope and South Pole Telescope experiments and consider the possibility of a universe with nonzero curvature. We first place new constraints on N-eff and Omega(k), with N-eff = 4.03 +/- 0.45 and 10(3)Omega(k) = -4.46 +/- 5.24. Thus, even when Omega(k) is allowed to vary, N-eff = 3 is still disfavored with 95% confidence. We then investigate the correlation between neutrino mass and curvature that shifts the 95% upper limit of Sigma m(v) < 0.45 eV to Sigma m(v) < 0.95 eV. Thus, the impact of assuming flatness in neutrino cosmology is significant and an essential consideration with future experiments.