  The standard calculations of the ground-state energy of a homogeneous Bose
gas rely on approximations which are physically reasonable but difficult to
control. Lieb and Yngvason [Phys. Rev. Lett. 80, 2504 (1998)] have proved
rigorously that the commonly accepted leading order term of the ground state
energy is correct in the zero-density-limit. Here, strong indications are given
that also the next to leading term is correct. It is shown that the first terms
obtained in a perturbative treatment provide contributions which are lost in
the Bogoliubov approach.
