The fate of (phantom) dark energy universe with string curvature corrections

We study the evolution of (phantom) dark energy universe by taking into account the higher-order string corrections to Einstein-Hilbert action with fixed dilaton and modulus fields. While the presence of a cosmological constant gives stable de Sitter fixed points in the cases of heterotic and bosonic strings, no stable de Sitter solutions exist when a phantom fluid is present. We find that the universe can exhibit a Big Crunch singularity with a finite time for type II string, whereas it reaches a Big Rip singularity for heterotic and bosonic strings. Thus the fate of dark energy universe crucially depends upon the type of string theory under consideration.