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 $V(T)sim M_{Pl}^4exp(-T/tau)$, the tachyon must start rolling at $Tsimeq 60tau$ 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.
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