2021/07/31 by Hemza Azri, Hemza Azrı, Salah Nasri
Mathematics · Physics and Astronomy · #Action (physics) #Advanced Differential Geometry Research #Antisymmetric relation #Antisymmetric tensor #Black Holes and Theoretical Physics #Classical mechanics #Connection (principal bundle) #Cosmology and Gravitation Theories #Curvature #Gauge theory #Geometry #Gravitation #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum gravity #Quantum mechanics #Ricci curvature #Scalar (mathematics) #Scalar curvature #Scalar field #Spin connection #Symmetrization #Theoretical physics #f(R) gravity #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.104.064028
published as Phys. Rev. D 104, 064028 (2021)
arxiv created 2021/09/09 · openalex publication_date 2021/09/09 · arxiv updated 2021/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In Eddington gravity, the action principle involves only the symmetric parts of the connection and the Ricci tensor, with a metric that emerges proportionally to the latter. Here, we relax this symmetric character, prolong the action with the antisymmetric parts of the Ricci term, and allow for various couplings with scalar fields. We propose two possible invariant actions formed by distinct combinations of the independent Ricci tensors and show that the generated metric must involve an additional antisymmetric part due to the relaxation of the symmetrization property. The comprehensive study shows that the second curvature influences the dynamics of the connection, hence its solution in terms of the metric, and the evolution of the scalar fields. These new dynamical features are expected to stand viable and to have interesting implications in domains where scalar fields are indispensable.