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

We propose a model of the evolution of the tachyonic scalar field over two phases in the universe. The field components do not interact in phase I, while in the subsequent phase II, they change flavours due to relative suppression of the radiation contribution. In phase II, we allow them to interact mutually with time-independent perturbation in their equations of state, as Shifted Cosmological Parameter (SCP) and Shifted Dust Matter (SDM). We determine the solutions of their scaling with the cosmic redshift in both phases. We further suggest the normalized Hubble function diagnostic, which, together with the low- and high-redshift $H(z)$ data and the concordance values of the present density parameters from the CMBR, BAO statistics etc., constrains the strength of interaction, by imposing the viable conditions to break degeneracy in 3-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 during structure formation, and it may lead to a future analysis of power spectrum in this model \emph{vis a vis} Warm Dark Matter (WDM) or $\Lambda$CDM models. We further calculate the influence of interaction in determining the age of the universe at the present epoch, within the degeneracy space of model parameters.