The Big Bang Nucleosynthesis (BBN) theory allows to calculate the abundance of isotopes createdin the early universe. Interestingly, the primordial abundance of deuterium deduced from observations of pristine gas at high redshifts is more accurate with respect to the computed value because the BBN calculation is affected by the paucity of data for the deuterium-burning reaction D(p,g)3He. In fact, only a single dataset is currently available in the BBN energy range, in which
the authors state systematic error of 9%. The concern for the D(p; g)3He cross section error is made worse by the fact that the theoretical and experimental values do not agree at the level of 20%. A new measurement is presently in progress at the LUNA (Laboratory for Underground Nuclear astrophysics) accelerator, operating deep underground at the Gran Sasso Laboratory, Italy. The main goal is the study of the D(p; g)3He cross section in the BBN energy range with accuracy. The LUNA measurement is described and preliminary results are discussed and compared with ab-initio calculations. The impact of this measurement in cosmology and particle physics is also highlighted. In particular, a precision measurement allows to derive the universal baryon density Wb with accuracy comparable to the one obtained by the PLANCK experiment. Finally, the accurate knowledge of the D(p; g)3He cross section increases the sensitivity to probe the existence of relativistic particles (e.g. sterile neutrinos, hot axions etc.) not foreseen in the standard model.