We investigate the tachyonic cosmological potential V(ϕ) in two
different cases of the quasi-exponential expansion of universe and discuss
various forms of interaction between the two components---matter and the
cosmological constant--- of the tachyonic scalar field, which leads to the
viable solutions of their respective energy densities. The distinction among
the interaction forms is shown to appear in the Om(x) diagnostic. Further,
the role of the high- and low-redshift observations of the Hubble parameter is
discussed to determine the proportionality constants and hence the correct form
of matter--cosmological constant interaction.Comment: 14 page