Stability of tardyons and tachyons in the rotating and expanding Universe

TL;DR

This paper investigates the stability and spectral properties of tardyonic and tachyonic fields in a rotating, expanding universe, revealing conditions under which tachyons can be stable and discussing implications for light particles like neutrinos.

Contribution

It demonstrates that tachyons are stable in a rotating, expanding universe if their mass is below a certain threshold, contrasting with their instability in Minkowski space.

Findings

Tachyons are stable in the universe if their mass is below a specific constant.

The spectrum of the Dirac field shows a discontinuity at zero wave vector component.

The upper bound on tachyon mass is many orders less than the electron mass.

Abstract

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, \emph{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 $k_z = 0$. Keywords: OPERA, superluminal neutrino.