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The primordial deuterium abundance probes fundamental physics during the Big Bang Nucleosynthesis and can be used to infer cosmological parameters. Observationally, the abundance can be measured using absorbing clouds along the lines of sight to distant quasars. Observations of the quasar PKS1937--101 contain two absorbers for which the deuterium abundance has previously been determined. Here we focus on the higher redshift one at $z_{abs} = 3.572$. We present new observations with significantly increased signal-to-noise ratio which enable a far more precise and robust measurement of the deuterium to hydrogen column density ratio, resulting in D/H = $2.62\pm0.05\times10^{-5}$. This particular measurement is of interest because it is among the most precise assessments to date and it has been derived from the second lowest column-density absorber [N(HI) $=17.9\mathrm{cm}^{-2}$] that has so-far been utilised for deuterium abundance measurements. The majority of existing high-precision measurements were obtained from considerably higher column density systems [i.e. N(HI) $>19.4\mathrm{cm}^{-2}$]. This bodes well for future observations as low column density systems are more common., Comment: 13 pages, 5 figures, 6 tables, accepted by MNRAS

The primordial deuterium abundance is an important tracer of the fundamental physics taking place during Big Bang Nucleosynthesis. It can be determined from absorption features along the line of sight to distant quasars. The quasar PKS1937-1009 contains two absorptions systems that have been used to measure the primordial deuterium abundance, the lower redshift one being at z_abs = 3.256. New observations of this absorber are of a substantially higher signal-to-noise and thus permit a significantly more robust estimate of the primordial deuterium abundance, leading to a D/H ratio of 2.45+/-0.28 x10^-5. Whilst the precision of the new measurement presented here is below that obtained from the recent cosmological parameter measurements by Planck, our analysis illustrates how a statistical sample obtained using similarly high spectral signal-to-noise can make deuterium a competitive and complementary cosmological parameter estimator and provide an explanation for the scatter seen between some existing deuterium measurements., Comment: 13 pages, 5 figures, matches version accepted by MNRAS