Stability in higher-derivative matter fields theories

TL;DR

This paper investigates the stability conditions of higher-derivative matter field theories, identifying parameter restrictions necessary to prevent instabilities in Minkowski space and avoiding tachyon-like issues.

Contribution

It provides a detailed analysis of stability criteria in higher-derivative matter theories using dynamical systems and quantum field theory approaches, revealing new parameter constraints.

Findings

Stability in Minkowski space requires <0.

Additional restriction >- for avoiding tachyon-like instabilities.

Derived explicit conditions for theory stability.

Abstract

We discuss possible instabilities in higher-derivative matter fields theories. These theories has two free parameters $\beta_1$ and $\beta_4$. By using dynamical system approach we explicitly demonstrate that for stability of Minkowski space in expanding Universe it is need condition $\beta_4<0$. By using quantum field theory approach we also find additional restriction for parameters $\beta_1>-\frac{1}{3}\beta_4$ which is need to avoid tachyon-like instability.