2009/04/30 by Thomas P. Sotiriou, Thomas P Sotiriou · 65 citations
Physics and Astronomy · #Affine connection #Black Holes and Theoretical Physics #Connection (principal bundle) #Cosmology #Cosmology and Gravitation Theories #Gravitation #Noncommutative and Quantum Gravity Theories #Torsion (gastropod) #astro-ph.CO #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/26/15/152001
published in Classical and Quantum Gravity 26(15), 152001 (IOP Publishing) · v2: slightly shortened version published in CQG as a Fast Track Communication
openalex publication_date 2009/07/15 · arxiv created 2009/07/16 · arxiv updated 2010/04/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
For both f ( R ) theories of gravity with an independent symmetric connection (no torsion), usually referred to as Palatini f ( R ) gravity theories, and for f ( R ) theories of gravity with torsion but no non-metricity, called U 4 theories, it has been shown that the independent connection can actually be eliminated algebraically, as long as this connection does not couple to matter. Remarkably, the outcome in both cases is the same theory, which is dynamically equivalent with an ω 0 = −3/2 Brans–Dicke theory. It is shown here that even for the most general case of an independent connection with both non-metricity and torsion, one arrives at exactly the same theory as in the more restricted cases. This generalizes the previous results and explains why assuming that either the torsion or the non-metricity vanishing ultimately leads to the same theory. It also demonstrates that f ( R ) actions cannot support an independent connection which carries dynamical degrees of freedom, irrespective of how general this connection is, at least as long as there is no connection–matter coupling.