  Consider a nonlinear wave equation for a massless scalar field with
self-interaction in the spatially flat de Sitter spacetime. We show that
blow-up in a finite time occurs for the equation with arbitrary power
nonlinearity as well as upper bounds of the lifespan of blow-up solutions.The
blow-up condition is the same as in the accelerated expanding
Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetime. We also show the same
results for the space derivative nonlinear term.
