We present strong bounds on the sum of three active neutrino masses ($sum m_{ u}$) 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 $Lambda CDM+sum m_{ u}$ model we find a upper bound of $sum m_{ u} <$ 0.152 eV at 95$%$ C.L. Adding the high-$l$ polarization data from Planck strengthens this bound to $sum m_{ u} <$ 0.118 eV, which is very close to the minimum required mass of $sum m_{ u} simeq$ 0.1 eV for inverted hierarchy. This bound is reduced to $sum m_{ u} <$ 0.110 eV when we also vary r, the tensor to scalar ratio ($Lambda CDM+r+sum m_{ u}$ model), and add an additional dataset, BK14, the latest data released from the Bicep-Keck collaboration. This bound is further reduced to $sum m_{ u} <$ 0.101 eV in a cosmology with non-phantom dynamical dark energy ($w_0 w_a CDM+sum m_{ u}$ model with $w(z)geq -1$ for all $z$). Considering the $w_0 w_a CDM+r+sum m_{ u}$ model and adding the BK14 data again, the bound can be even further reduced to $sum m_{ u} <$ 0.093 eV. For the $w_0 w_a CDM+sum m_{ u}$ model without any constraint on $w(z)$, the bounds however relax to $sum m_{ u} <$ 0.276 eV. Adding a prior on the Hubble constant ($H_0 = 73.24pm 1.74$ km/sec/Mpc) from Hubble Space Telescope (HST), the above mentioned bounds further improve to $sum m_{ u} <$ 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)
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