  We define gravitational mass in asymptotically de Sitter space-times with
compactified dimension. It was shown that the mass can be negative for
space-time with matter spreading beyond the cosmological horizon scale or large
outward `momentum' in four dimension. We give simple examples with negative
energy in higher dimensions even if the matter is not beyond horizon or system
does not have large `momentum'. They do not have the lower bound on the mass.
We also give a positive energy argument in higher dimensions and realise that
elementary fermion cannot exist in our examples.
