  Recent astronomical data have provided the primordial deuterium abundance
with percent precision. As a result, Big Bang nucleosynthesis may provide a
constraint on the universal baryon to photon ratio that is as precise as, but
independent from, analyses of the cosmic microwave background. However, such a
constraint requires that the nuclear reaction rates governing the production
and destruction of primordial deuterium are sufficiently well known. Here, a
new measurement of the $^2$H($p,\gamma$)$^3$He cross section is reported. This
nuclear reaction dominates the error on the predicted Big Bang deuterium
abundance. A proton beam of 400-1650keV beam energy was incident on solid
titanium deuteride targets, and the emitted $\gamma$-rays were detected in two
high-purity germanium detectors at angles of 55$^\circ$ and 90$^\circ$,
respectively. The deuterium content of the targets has been obtained in situ by
the $^2$H($^3$He,$p$)$^4$He reaction and offline using the Elastic Recoil
Detection method. The astrophysical S-factor has been determined at center of
mass energies between 265 and 1094 keV, addressing the uppermost part of the
relevant energy range for Big Bang nucleosynthesis and complementary to ongoing
work at lower energies. The new data support a higher S-factor at Big Bang
temperatures than previously assumed, reducing the predicted deuterium
abundance.
