Interacting closed string tachyon with modified Chaplygin gas and its stability

In this paper, we have considered a closed string tachyon model with a constant dilaton field and interacted it with Chaplygin gas for evaluating cosmology parameters. The model has been studied in 26 dimensions, with 22 dimensions related to compactification on an internal nonflat space and its other 4 dimensions related to the Friedmann-Lemaître-Robertson-Walker metric. By taking the internal curvature as a negative constant, we reconstructed the closed string tachyon potential in terms of tachyon field as a quartic equation. The tachyon field and the scale factor have been achieved as a function of time evolution and geometry of curved space where the behavior of the scale factor describes an accelerated expansion of the Universe. Next, we discussed the stability of our model by introducing a sound speed factor, which must be, in our case, a positive function. By drawing sound speed against time evolution, we investigated stability conditions for a nonflat universe in its three stages: early, late, and future time. As a result we shall see that in these cases there remains an instability at early time and a stability point at late time.