Stability of tardyons and tachyons in the rotating and expanding Universe

In the present paper we analyze the spectrum of quasinormal modes for massive scalar and Dirac fields, allowing for both tardyonic (${\mu }^2>0$) and tachyonic (${\mu }^2<0$) masses, in the expanding and rotating cosmological background. The spectrum found shows a number of peculiar features, which are absent in the Minkowski space-time. A hypothetical particle that moves faster than light, a tachyon, is known to be classically unstable in the Minkowski space-time. This instability has its analog at the quantum level: small vacuum fluctuations of the field lead to the unbounded growth of the amplitude, so that the appearance of the real tachyons in the spectrum means that there is catastrophic instability in the theory. It has been conjectured a long time ago that possibly the lightest particles with nonzero mass, the neutrino, may be a tachyon. Here we shall show that in the rotating and expanding Universe tachyons are stable if their mass is less than some constant, which is related to the Universe’s rotation and expansion scales. The current upper bound on the rotation scale gives us a very small upper bound on the tachyon’s mass which is many orders less than the mass of the electron. This might explain why only very light particles have the chance of becoming tachyons. It is shown that the spectrum of the “normal” (${\mu }^2>0$) Dirac field has a discontinuity as a function of the $z$ component of the wave vector $k_z$ at $k_z=0$.

Figure 1

Left panel: Real parts of Dirac quasinormal modes as functions of $F(k_z)$ for $B=1/2$. Upper (positive real part) curves correspond to $m=-1$, lower (negative real part) correspond to $m=+1$. Right panel shows $k_z$ as a function of $\mu$ for which $F(k_z)$ is zero.

Figure 2

Real parts of Dirac quasinormal modes as functions of $k_z$ for $B=1/2$, $\mu =0$ (left panel) and $a\mu =2$ (right panel).