Vector theories in cosmology

2009/12/02 by Gilles Esposito-Farèse, Gilles Esposito-Farese, Cyril Pitrou +2 · 127 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Classical mechanics #Cosmology #Cosmology and Gravitation Theories #Curvature #Field (mathematics) #Geometry #Gravitation #Hamiltonian (control theory) #Magnetic field #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum mechanics #Theoretical physics #Vector field #Vector potential #astro-ph.CO #gr-qc

paper · pdf · doi:10.1103/physrevd.81.063519

published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 81(6) (American Physical Society) · 17 pages, no figure

arxiv created 2009/12/02 · openalex publication_date 2010/03/15 · arxiv updated 2010/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

This article provides a general study of the Hamiltonian stability and the hyperbolicity of vector field models involving both a general function of the Faraday tensor and its dual, f(F²,F\stackrel\texttildelowF), as well as a Proca potential for the vector field, V(A²). In particular it is demonstrated that theories involving only f(F²) do not satisfy the hyperbolicity conditions. It is then shown that in this class of models, the cosmological dynamics always dilutes the vector field. In the case of a nonminimal coupling to gravity, it is established that theories involving Rf(A²) or Rf(F²) are generically pathologic. To finish, we exhibit a model where the vector field is not diluted during the cosmological evolution, because of a nonminimal vector field-curvature coupling which maintains second-order field equations. The relevance of such models for cosmology is discussed.

Citations

• Examination of Evidence for a Preferred Axis in the Cosmic Radiation Anisotropy
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• General Relativity and the Einstein Equations
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• Anisotropic inflation from vector impurity
• Superluminal Behavior, Causality, and Instability
• Spacetime noncommutativity and antisymmetric tensor dynamics in the early Universe
• Cosmological electromagnetic fields and dark energy
• Linear perturbations in vector inflation and stability issues
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• Primordial statistical anisotropy generated at the end of inflation
• k-Essence, superluminal propagation, causality and emergent geometry
• Asymmetries in the Local Curvature of the Wilkinson Microwave Anisotropy Probe Data
• First‐Year Wilkinson Microwave Anisotropy Probe ( WMAP ) Observations: Determination of Cosmological Parameters
• P-nflation: generating cosmic Inflation with p-forms
• The galileon as a local modification of gravity
• No large-angle correlations on the non-Galactic microwave sky
• A tensor--vector--scalar framework for modified dynamics and cosmic dark matter
• Covariant Galileon
• Aether unleashed

Cited by

• On hyperbolicity violations in cosmological models with vector fields
• Dark matter via massive bigravity
• On the 4D generalized Proca action for an Abelian vector field
• Cosmology in doubly coupled massive gravity: Constraints from SNIa, BAO and CMB
• Bianchi cosmologies with p -form gauge fields
• Anisotropic power-law inflation
• The ghost of vector fields in compact stars

Related

• Cosmology with vector distortion
• Aether unleashed
• Vector field models of inflation and dark energy
• On scalar and vector fields coupled to the energy-momentum tensor
• Theory space and stability analysis of General Relativistic cosmological solutions in modified gravity