  We examine whether tachyon matter is a viable candidate for the cosmological
dark matter. First, we demonstrate that in order for the density of tachyon
matter to have an acceptable value today, the magnitude of the tachyon
potential energy at the onset of rolling must be finely tuned. For a tachyon
potential $V(T)\sim M_{Pl}^4\exp(-T/\tau)$, the tachyon must start rolling at
$T\simeq 60\tau$ in order for the density of tachyon matter today to satisfy
$\Omega_{T,0}\sim 1$, provided that standard big bang cosmology begins at the
same time as the tachyon begins to roll. In this case, the value of
$\Omega_{T,0}$ is exponentially sensitive to $T/\tau$ at the onset of rolling,
so smaller $T/\tau$ is unacceptable, and larger $T/\tau$ implies a tachyon
density that is too small to have interesting cosmological effects. If instead
the universe undergoes a second inflationary epoch after the tachyon has
already rolled considerably, then the tachyon can begin with $T$ near zero, but
the increase of the scale factor during inflation must still be finely tuned in
order for $\Omega_{T,0} \sim 1$. Second, we show that tachyon matter, unlike
quintessence, can cluster gravitationally on very small scales. If the starting
value of $T/\tau$ is tuned finely enough that $\Omega_{T,0}\sim 1$, then
tachyon matter clusters more or less identically to pressureless dust. Thus, if
the fine-tuning problem can be explained, tachyon matter is a viable candidate
for cosmological dark matter.
