A Matter with an effective EoS interacting with a tachynic field in an accelerating Universe

We consider a fluid described by a parameterized EoS of the general form $P=(\gamma -1)\rho +p_0+{\omega }_{H}H+{\omega }_{H2}{H}^2+{\omega }_{dH}\dot{H}$ \cite{Ren}, where $p_0$, ${\omega }_H$, ${\omega }_{H2}$ and ${\omega }_{dH}$ are free parameters of the model, interacting with a Tachyonic field with a relativistic Lagrangian $L_{TF}=-V(\varphi )\sqrt{1-{\mathrm{\partial }}_i\varphi {\mathrm{\partial }}^i\varphi }$. The acceleration of the Universe described by a scale factor $a(t)=t^n,(n>1)$. Under consideration of different forms of interaction the field $\varphi$ and the potential $V(\varphi )$ are recovered and graphical analysis performed. For illustration purposes we fixed values of parameters of the models to provide $V \rightarrow 0$forlaterstagesofevolution,when$t \rightarrow \infty$.