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In this paper, we consider the stability of cylindrical wormholes duringevolution of universe from inflation to late time acceleration epochs. We showthat there are two types of cylindrical wormholes. The first type is producedat the corresponding point where k black F-strings are transited to BIonconfiguration. This wormhole transfers energy from extra dimensions into ouruniverse, causes inflation, loses it's energy and vanishes. The second type ofcylindrical wormhole is created by a tachyonic potential and causes a new phaseof acceleration. We show that wormhole parameters grow faster than the scalefactor in this era, overtake it at ripping time and lead to the destruction ofuniverse at big rip singularity.

Stability of cylindrical thin shell wormhole during evolution of universe from inflation to late time acceleration