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 $P=(γ-1)ρ+p_{0}+ω_{H}H+ω_{H2}H^{2}+ω_{dH}\dot{H}$ \cite{Ren}, where $p_{0}$, $ω_{H}$, $ω_{H2}$ and $ω_{dH}$ are free parameters of the model, interacting with a Tachyonic field with a relativistic Lagrangian $L_{TF}=-V(ϕ)\sqrt{1-\partial_{i}ϕ\partial^{i}ϕ}$. 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 $ϕ$ and the potential $V(ϕ)$ are recovered and graphical analysis performed. For illustration purposes we fixed values of parameters of the models to provide $V \rightarrow 0$ for later stages of evolution, when $t \rightarrow \infty$.

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