Updated Bounds on Sum of Neutrino Masses in Various Cosmological Scenarios

We present strong bounds on the sum of three active neutrino masses ($\sum m_{\nu}$) in various cosmological models. We use the following baseline datasets: CMB temperature data from Planck 2015, BAO measurements from SDSS-III BOSS DR12, the newly released SNe Ia dataset from Pantheon Sample, and a prior on the optical depth to reionization from 2016 Planck Intermediate results. We constrain cosmological parameters in $\Lambda CDM$ model with 3 massive active neutrinos. For this $\Lambda CDM+\sum m_{\nu}$ model we find a upper bound of $\sum m_{\nu} <$ 0.152 eV at 95$\%$ C.L. Adding the high-$l$ polarization data from Planck strengthens this bound to $\sum m_{\nu} <$ 0.118 eV, which is very close to the minimum required mass of $\sum m_{\nu} \simeq$ 0.1 eV for inverted hierarchy. This bound is reduced to $\sum m_{\nu} <$ 0.110 eV when we also vary r, the tensor to scalar ratio ($\Lambda CDM+r+\sum m_{\nu}$ model), and add an additional dataset, BK14, the latest data released from the Bicep-Keck collaboration. This bound is further reduced to $\sum m_{\nu} <$ 0.101 eV in a cosmology with non-phantom dynamical dark energy ($w_0 w_a CDM+\sum m_{\nu}$ model with $w(z)\geq -1$ for all $z$). Considering the $w_0 w_a CDM+r+\sum m_{\nu}$ model and adding the BK14 data again, the bound can be even further reduced to $\sum m_{\nu} <$ 0.093 eV. For the $w_0 w_a CDM+\sum m_{\nu}$ model without any constraint on $w(z)$, the bounds however relax to $\sum m_{\nu} <$ 0.276 eV. Adding a prior on the Hubble constant ($H_0 = 73.24\pm 1.74$ km/sec/Mpc) from Hubble Space Telescope (HST), the above mentioned bounds further improve to $\sum m_{\nu} <$ 0.117 eV, 0.091 eV, 0.085 eV, 0.082 eV, 0.078 eV and 0.247 eV respectively. This substantial improvement is mostly driven by a more than 3$\sigma$ tension between Planck 2015 and HST measurements of $H_0$ and should be taken cautiously. (abstract abridged)