The 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 \sum m_\nu, and the curvature of the universe \Omega_k, it is useful to investigate the current constraints in the framework of a non-flat universe. In this paper we update the constraints on neutrino parameters by making use of the latest cosmic microwave background (CMB) data from the ACT and SPT experiments and consider the possibility of a universe with non-zero 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 \sum m_\nu < 0.45 eV to \sum m_\nu < 0.95 eV. Thus, the impact of assuming flatness in neutrino cosmology is significant and an essential consideration with future experiments.