Tachyonic thermal excitations and causality

Abstract

We consider an ideal Fermi gas of tachyonic thermal excitations as a continuous medium and establish when it satisfies the causality condition. At high temperature the sound speed is always subluminal $c_s<1$, but there is no stable form of tachyon matter below the critical temperature $T_c<0.23m$ that depends on the tachyon mass $m$. The pressure $P$ and energy density $E$ cannot be arbitrary small, but $P$ can exceed $E$, and $P=2.36E$ when $T\rightarrow T_c$.