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

By B. Himmetoḡlu, C. Contaldi, Marco Peloso. 2009

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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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/9c772e6a9275ad464d6973221b20712e2e09e036

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Citations in the corpus

A systematic approach to generalisations of General Relativity and their cosmological implications (2018, background): “The encountered instabilities for some of these models make them cosmologically unviable [244].”
Adding helicity to inflationary magnetogenesis (2014, background): “Since mechanisms that violate gauge invariance generally give rise to ghost-like instabilities [5, 6], most of the attention has gone to two mechanisms that preserve gauge invariance.”
Observable non-gaussianity from gauge field production in slow roll inflation, and a challenging connection with magnetogenesis (2012, background): “This second case, however, introduces a longitudinal vector component, which turns out to be a ghost [31, 32].”
Cosmology and Fundamental Physics with the Euclid Satellite (2012, background): “For some of these models there are actually some instability issues about the evolution of the primordial longitudinal perturbation modes of the vector field [587, 586].”