2015/09/30 by Jose Beltrán Jiménez, Tomi S. Koivisto, Tomi Koivisto · 1 citation
Mathematics · Physics and Astronomy · #Affine connection #Affine transformation #Black Holes and Theoretical Physics #Conformal field theory #Conformal geometry #Conformal map #Cosmology and Gravitation Theories #Curvature #Differential geometry #Einstein tensor #Gauge theory #Geometry #Killing vector field #Kinetic term #Mathematical physics #Mathematics #Physics #Quadratic equation #Quantum mechanics #Riemann curvature tensor #Scalar field #Solar and Space Plasma Dynamics #Spacetime #Spin connection #Torsion (gastropod) #Vector field #Weyl tensor #astro-ph.CO #gr-qc #hep-th
paper · pdf · doi:10.1016/j.physletb.2016.03.047
5 pages, 1 table, 0 figures. V2: Added the general quadratic theory
arxiv created 2016/01/06 · openalex publication_date 2016/03/22 · arxiv updated 2016/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Spacetime with general linear vector distortion is introduced. Thus, the torsion and the nonmetricity of the affine connection are assumed to be proportional to a vector field (and not its derivatives). The resulting two-parameter family of non-Riemannian geometries generalises the conformal Weyl geometry and some other interesting special cases. Taking into account the leading nonlinear correction to the Einstein–Hilbert action results uniquely in the one-parameter extension of the Starobinsky inflation known as the alpha-attractor. The most general quadratic curvature action introduces, in addition to the canonical vector kinetic term, novel ghost-free vector-tensor interactions.