We study the cosmological evolution of a tachyon scalar field T with aDirac-Born-Infeld type lagrangian and potential V(T) coupled to a canonicallynormalized scalar field \phi with an arbitrary interaction term B(T,\phi) inthe presence of a barotropic fluid $\rb$, which can be matter or radiation. Theforce between the barotropic fluid and the scalar fields is only gravitational.We show that the dynamics is completely determine by only three parameters L1 =- V_T/ V^{3/2}, L2= - B_T /B^{3/2} and L3 =-B_{\phi}/B. We determineanalytically theconditions for $\lm_i$ under which the energy density of T,\phi and $\rb$ have the same redshift. We study the behavior of T and \phi inthe asymptotic limits for L_i and we show the numerical solution for differentinteresting cases. The effective equation of state for the tachyon field changes due to theinteraction with the scalar field and we show that it is possible for a tachyonfield to redshift as matter in the absence of an interaction term B and asradiation when B is turned on. This result solves then the tachyonic matterproblem.
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