  We consider the effect on Big Bang Nucleosynthesis (BBN) of new measurements
of the $d(p,\gamma){}^3$He cross section by the LUNA Collaboration. These have
an important effect on the primordial abundance of D/H which is also sensitive
to the baryon density at the time of BBN. We have re-evaluated the thermal rate
for this reaction, using a world average of cross section data, which we
describe with model-independent polynomials; our results are in good agreement
with a similar analysis by LUNA. We then perform a full likelihood analysis
combining BBN and Planck cosmic microwave background (CMB) likelihood chains
using the new rate combined with previous measurements and compare with the
results using previous rates. Concordance between BBN and CMB measurements of
the anisotropy spectrum using the old rates was excellent. The predicted
deuterium abundance at the Planck value of the baryon density was $({\rm
D/H})_{\rm BBN+CMB}^{\rm old} = (2.57 \pm 0.13) \times 10^{-5}$ which can be
compared with the value determined from quasar absorption systems $({\rm
D/H})_{\rm obs} = (2.55 \pm 0.03) \times 10^{-5} $. Using the new rates we find
$({\rm D/H})_{\rm BBN+CMB} = (2.51 \pm 0.11) \times 10^{-5}$. We thus find
consistency among BBN theory, deuterium and ${}^4$He observations, and the CMB,
when using reaction rates fit in our data-driven approach. We also find that
the new reaction data tightens the constraints on the number of relativistic
degrees of freedom during BBN, giving the effective number of light neutrino
species $N_\nu = 2.880 \pm 0.144$ in good agreement with the Standard Model of
particle physics. Finally, we note that the observed deuterium abundance
continues to be more precise than the BBN+CMB prediction, whose error budget is
now dominated by $d(d,n){}^3$He and $d(d,p){}^{3}{\rm H}$.
