  In the present work the power spectrum of a particular class of tachyon
fields is compared with the one corresponding to a cosmological constant model.
This is done for different barotropic indexes $\gamma_0$ and the background
space time is assumed to be of the spatially flat Friedmann-Robertson-Walker
type. The differential equation describing the perturbations is solved
numerically and the power spectrum at the scale factor value $a=1$ is plotted
for each case. The result is that the power spectrum of the standard tachyon
field differs in many magnitude orders from the $\Lambda$CDM. However, the one
with $\gamma_0=1.91$, which corresponds to a complementary tachyon field,
coincides fairly well with the concordance model. Therefore, we conclude that
the perturbed solutions constitute an effective method to distinguish between
the different $\gamma_0$ values for the tachionization $\Lambda$CDM model and
the fiducial model. The Statefinder parameters $\{r, s\}$, measuring the
deviations of the analysed model from the concordance model, are also
explicitly calculated. Our result suggest that, depending on the value of
$\gamma_0$, these models can explain the observed expansion history or the
perturbation power spectrum of the universe, but they may have problems in
describing both features simultaneously.
