Chinese Acad Sci, Inst High Energy Phys, Beijing 100049, Peoples R China
; Chinese Acad Sci, Inst Theoret Phys, Beijing 100080, Peoples R China
; USTC, Interdisciplinary Ctr Theoret Study China, Hefei 230027, Peoples R China
We investigate the condition for eternal inflation to take place in the noncommutative spacetime. We find that the possibility for eternal inflation's happening is greatly suppressed in this case. If eternal inflation cannot happen in the low energy region where the noncommutativity is very weak (the UV region), it will never happen during the whole inflationary history. Based on these conclusions, we argue that an initial condition for eternal inflation is available from the property of spacetime noncommutativity.