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We propose a model of the evolution of the tachyonic scalar field over twophases in the universe. The field components do not interact in phase I, whilein the subsequent phase II, they change flavours due to relative suppression ofthe radiation contribution. In phase II, we allow them to interact mutuallywith time-independent perturbation in their equations of state, as ShiftedCosmological Parameter (SCP) and Shifted Dust Matter (SDM). We determine thesolutions of their scaling with the cosmic redshift in both phases. We furthersuggest the normalized Hubble function diagnostic, which, together with thelow- and high-redshift $H(z)$ data and the concordance values of the presentdensity parameters from the CMBR, BAO statistics etc., constrains the strengthof interaction, by imposing the viable conditions to break degeneracy in3-parameter $(\gamma, \varepsilon, \dot{\phi}^2)$ space. The range of redshifts$(z=0.1$ to $z=1.75)$ is chosen to highlight the role of interaction duringstructure formation, and it may lead to a future analysis of power spectrum inthis model \emph{vis a vis} Warm Dark Matter (WDM) or $\Lambda$CDM models. Wefurther calculate the influence of interaction in determining the age of theuniverse at the present epoch, within the degeneracy space of model parameters.

Evolution of shifted cosmological parameter and shifted dust matter in a two-phase tachyonic field universe