  In this work we determine the power spectrum of the gravitational potential
of the primordial fluctuations for an inflationary model whose \emph{inflaton}
is a non-canonical scalar field of the tachyon-type. The respective background
field equations for an inverse-square potential produce a power-law inflation,
and it is explicitly shown that for such a potential the power spectrum tends
to be scale-independent for highly accelerated regimes in the inflationary
expansion.
