Interacting closed string tachyon with modified Chaplygin gas and its stability

In this paper, we have considered 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 $26$-dimensional that its $22$-dimensional is related to compactification on an internal non-flat space and its other $4$-dimensions is related to FLRW metric. By taking the internal curvature as a negative constant, we obtained the closed string tachyon potential as a quartic equation. The tachyon field and the scale factor have been achieved as functional of time evolution and geometry of curved space where the behaviour 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 one must be, in our case, a positive function. By drawing sound speed against time evolution we investigated stability conditions for non-flat universe in its three stages: early, late and future time. As a result we shall see that in these cases remains an instability at early time and a stability point at late time.