Cosmographic analysis of the dynamics of universe in higher dimensional compactified space with Tachyonic field

In this work, the considered model is contained in higher dimensional compactified space in the form of M⁴ × M⁶, where M⁶ is compact inner space. Since, for a higher dimensional cosmological model, Tachyon matter is an automatic and fantastic choice, we have supposed that the scalar field is driven by Tachyon together with the higher dimensional cosmological constant ⊼. Our observation is that the theory provides a good solution for the cosmological scale factor of the present universe. Here, it is important that the forms of the tachyonic field ϕ and potential V are simple trigonometric hyperbolic functions. We study the cosmographical parameters like equation of state parameter, statefinder parameters, jerk, snap, and lerk parameters. The graphical representations of cosmological parameters show the overall evolution of the universe under a tachyonic field in a higher dimensional model. The classical stability of the model due to small perturbations both for dark energy and metric are examined by the study of the square speed of sound and by the linear perturbation method. We also analyzed the model in ω−ω′ and r−s cosmological plane. (author)