Ghost Instabilities in Self-Interacting Vector Fields: The Problem with Proca Fields.

Area of Science:

• Particle Physics
• Theoretical Physics
• Cosmology

Background:

• Massive vector fields are crucial in particle physics, mediating weak interactions, acting as dark matter candidates, and describing photons in plasma.
• The Proca equation describes massive vector fields, but modifications for self-interactions are explored here.

Purpose of the Study:

• To investigate the stability of massive vector fields with self-interactions by modifying the Proca equation.
• To analyze the impact of self-interactions on vector field dynamics, particularly concerning instabilities.
• To explore the implications for various physical phenomena, including dark matter and astrophysical events.

Main Methods:

• Replacing the standard mass term in the Proca equation with a general self-interaction potential.
• Analyzing the emergence of ghost instabilities in this modified theory.
• Simulating the evolution of a self-interacting Proca field on a Kerr black hole background.

Main Results:

• Self-interactions in massive vector fields inevitably introduce ghost instabilities, similar to those in modified gravity theories.
• Nonperturbative dynamics do not prevent these instabilities; instead, superradiant instability on a Kerr background amplifies them.
• Instabilities are triggered in finite time once self-interaction becomes significant, even if the system initially behaves like a massive field.

Conclusions:

• The presence of ghost instabilities in self-interacting massive vector fields has significant implications for theoretical models.
• These findings challenge the viability of certain vector dark matter models and the formation of spin-one bosenovae.
• The study highlights the importance of considering field self-interactions and their stability in various physical contexts, from particle physics to astrophysics.