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Consider a nonlinear wave equation for a massless scalar field withself-interaction in the spatially flat Friedmann-Lema\^{i}tre-Robertson-Walkerspacetimes. For the case of accelerated expansion, we show that blow-up in afinite time occurs for the equation with arbitrary power nonlinearity as wellas upper bounds of the lifespan of blow-up solutions. Comparing to the case ofthe Minkowski spacetime, we discuss how the scale factor affects the lifespanof blow-up solutions of the equation.

Blow up of solutions of semilinear wave equations in accelerated expanding Friedmann-Lema\^{i}tre-Robertson-Walker spacetime