The problem with Proca: ghost instabilities in self-interacting vector fields

Abstract

Massive vector fields feature in several areas of particle physics, e.g., as carriers of weak interactions, dark matter candidates, or as an effective description of photons in a plasma. Here we investigate vector fields with self-interactions by replacing the mass term in the Proca equation with a general potential. We show that this seemingly benign modification inevitably introduces ghost instabilities of the same kind as those recently identified for vector-tensor theories of modified gravity (but in this simpler, minimally coupled theory). It has been suggested that nonperturbative dynamics may drive systems away from such instabilities. We demonstrate that this is not the case by evolving a self-interacting Proca field on a Kerr background, where it grows due to the superradiant instability. The system initially evolves as in the massive case, but instabilities are triggered in a finite time once the self-interaction becomes significant. These instabilities have implications for the formation of condensates of massive, self-interacting vector bosons, the possibility of spin-one bosenovae, vector dark matter models, and effective models for interacting photons in a plasma.

10 pages, 5 figures, updated to accepted version

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• Coordinate singularities of self-interacting vector field theories
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• Big Bang Nucleosynthesis constraints on the cosmological evolution in a Universe with a Weylian Boundary
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• Multipole analysis on stationary massive vector and symmetric tensor fields
• Aspects of time evolution in $p$-form field theories
• Black hole destabilization via trapped quasi-normal modes
• Linear stability of nonrelativistic Proca stars
• Stationary Einstein-vector-Gauss-Bonnet black holes
• Internal symmetry to the rescue: well-posed 1+1 evolution of self-interacting vector fields
• The well-posedness of the Cauchy problem for self-interacting vector fields
• The intrinsic pathology of self-interacting vector fields