  We present a novel approach to the Bogoliubov theory of dilute Bose gases,
allowing for an elementary derivation of the celebrated Lee-Huang-Yang formula
in the Gross-Pitaevskii regime. Furthermore, we identify the low lying
excitation spectrum beyond the Gross-Pitaevskii scaling, extending a recent
result [3] to significantly more singular scaling regimes. Finally, we provide
an upper bound on the ground state energy in the Gross-Pitaevskii regime that
captures the correct expected order of magnitude beyond the Lee-Huang-Yang
formula.
