  We consider homogeneous Bose gas in a large cubic box with periodic boundary
conditions, at zero temperature. We analyze its excitation spectrum in a
certain kind of a mean field infinite volume limit. We prove that under
appropriate conditions the excitation spectrum has the form predicted by the
Bogoliubov approximation. Our result can be viewed as an extension of the
result of R. Seiringer (arXiv:1008.5349 [math-ph]) to large volumes.
