We study cosmological solutions in the effective heterotic string theory with α′-correction terms in the string frame. It is pointed out that the effective theory has an ambiguity via field redefinition and we analyze generalized effective theories due to this ambiguity. We restrict our analysis to the effective theories which give equations of motion of second order in the derivatives, just as "Galileon" field theory. This class of effective actions contains two free coupling constants. We find de Sitter solutions as well as the power-law expanding universes in our four-dimensional Einstein frame. The accelerated expanding universes are always attractors in the present dynamical system.
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