  In this work we derive some blow-up results for semilinear wave equations
both in de Sitter and anti-de Sitter spacetimes. By requiring suitable
conditions on a time-dependent factor in the nonlinear term, we prove the
blow-up in finite time of the spatial averages of local in time solutions. In
particular, we derive a sequence of lower bound estimates for the spatial
average by combining a suitable slicing procedure with an iteration frame for
this time-dependent functional.
