Ghost instabilities of cosmological models with vector fields nonminimally coupled to the curvature

Journal Article · Tue Dec 15 00:00:00 EST 2009 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.80.123530· OSTI ID:21313585

Himmetoglu, Burak; Peloso, Marco ^[1]; Contaldi, Carlo R ^[2]

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1. School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455 (United States)
2. Theoretical Physics, Blackett Laboratory, Imperial College, London, SW7 2BZ (United Kingdom)

We prove that many cosmological models characterized by vectors nonminimally coupled to the curvature (such as the Turner-Widrow mechanism for the production of magnetic fields during inflation, and models of vector inflation or vector curvaton) contain ghosts. The ghosts are associated with the longitudinal vector polarization present in these models and are found from studying the sign of the eigenvalues of the kinetic matrix for the physical perturbations. Ghosts introduce two main problems: (1) they make the theories ill defined at the quantum level in the high energy/subhorizon regime (and create serious problems for finding a well-behaved UV completion), and (2) they create an instability already at the linearized level. This happens because the eigenvalue corresponding to the ghost crosses zero during the cosmological evolution. At this point the linearized equations for the perturbations become singular (we show that this happens for all the models mentioned above). We explicitly solve the equations in the simplest cases of a vector without a vacuum expectation value in a Friedmann-Robertson-Walker geometry, and of a vector with a vacuum expectation value plus a cosmological constant, and we show that indeed the solutions of the linearized equations diverge when these equations become singular.

• OSTI ID: 21313585
• Journal Information: Physical Review. D, Particles Fields, Vol. 80, Issue 12; Other Information: DOI: 10.1103/PhysRevD.80.123530; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
COSMOLOGICAL CONSTANT
COSMOLOGICAL MODELS
DISTURBANCES
EIGENVALUES
EQUATIONS
EVOLUTION
EXPECTATION VALUE
INFLATIONARY UNIVERSE
INSTABILITY
MAGNETIC FIELDS
MATHEMATICAL SOLUTIONS
PERTURBATION THEORY
POLARIZATION
VECTOR FIELDS