  The total cross section for radiative neutron capture on a proton, $np \to d
\gamma$, is evaluated at big bang nucleosynthesis (BBN) energies. The
electromagnetic transition amplitudes are calculated up to next-to leading
order within the framework of pionless effective field theory with dibaryon
fields. We also calculate the $d\gamma\to np$ cross section and the photon
analyzing power for the $d\vec{\gamma}\to np$ process from the amplitudes. The
values of low energy constants that appear in the amplitudes are estimated by a
Markov Chain Monte Carlo analysis using the relevant low energy experimental
data. Our result agrees well with those of other theoretical calculations
except for the $np\to d\gamma$ cross section at some energies estimated by an
R-matrix analysis. We also study the uncertainties in our estimation of the
$np\to d\gamma$ cross section at relevant BBN energies and find that the
estimated cross section is reliable to within $\sim$1% error.
