The trivial role of torsion in projective invariant theories of gravity with non-minimally coupled matter fields
We study a large family of metric-affine theories with a projective symmetry, including non-minimally coupled matter fields which respect this invariance. The symmetry is straightforwardly realised by imposing that the connection only enters through the symmetric part of the Ricci tensor, even in th...
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2017
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02649381_v34_n23_p_Alfonso http://hdl.handle.net/20.500.12110/paper_02649381_v34_n23_p_Alfonso |
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paper:paper_02649381_v34_n23_p_Alfonso2023-06-08T15:23:29Z The trivial role of torsion in projective invariant theories of gravity with non-minimally coupled matter fields metric-affine theories modified gravity non-minimal couplings torsion We study a large family of metric-affine theories with a projective symmetry, including non-minimally coupled matter fields which respect this invariance. The symmetry is straightforwardly realised by imposing that the connection only enters through the symmetric part of the Ricci tensor, even in the matter sector. We leave the connection completely free (including torsion), and obtain its general solution as the Levi-Civita connection of an auxiliary metric, showing that the torsion only appears as a projective mode. This result justifies the widely used condition of setting vanishing torsion in these theories as a simple gauge choice. We apply our results to some particular cases considered in the literature, including the so-called Eddington-inspired-Born-Infeld theories among others. We finally discuss the possibility of imposing a gauge fixing where the connection is metric compatible, and comment on the genuine character of the non-metricity in theories where the two metrics are not conformally related. © 2017 IOP Publishing Ltd. 2017 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02649381_v34_n23_p_Alfonso http://hdl.handle.net/20.500.12110/paper_02649381_v34_n23_p_Alfonso |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
metric-affine theories modified gravity non-minimal couplings torsion |
| spellingShingle |
metric-affine theories modified gravity non-minimal couplings torsion The trivial role of torsion in projective invariant theories of gravity with non-minimally coupled matter fields |
| topic_facet |
metric-affine theories modified gravity non-minimal couplings torsion |
| description |
We study a large family of metric-affine theories with a projective symmetry, including non-minimally coupled matter fields which respect this invariance. The symmetry is straightforwardly realised by imposing that the connection only enters through the symmetric part of the Ricci tensor, even in the matter sector. We leave the connection completely free (including torsion), and obtain its general solution as the Levi-Civita connection of an auxiliary metric, showing that the torsion only appears as a projective mode. This result justifies the widely used condition of setting vanishing torsion in these theories as a simple gauge choice. We apply our results to some particular cases considered in the literature, including the so-called Eddington-inspired-Born-Infeld theories among others. We finally discuss the possibility of imposing a gauge fixing where the connection is metric compatible, and comment on the genuine character of the non-metricity in theories where the two metrics are not conformally related. © 2017 IOP Publishing Ltd. |
| title |
The trivial role of torsion in projective invariant theories of gravity with non-minimally coupled matter fields |
| title_short |
The trivial role of torsion in projective invariant theories of gravity with non-minimally coupled matter fields |
| title_full |
The trivial role of torsion in projective invariant theories of gravity with non-minimally coupled matter fields |
| title_fullStr |
The trivial role of torsion in projective invariant theories of gravity with non-minimally coupled matter fields |
| title_full_unstemmed |
The trivial role of torsion in projective invariant theories of gravity with non-minimally coupled matter fields |
| title_sort |
trivial role of torsion in projective invariant theories of gravity with non-minimally coupled matter fields |
| publishDate |
2017 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02649381_v34_n23_p_Alfonso http://hdl.handle.net/20.500.12110/paper_02649381_v34_n23_p_Alfonso |
| _version_ |
1768546582492348416 |