PT Journal
AU Alfonso, VI
   Bejarano, C
   Beltran Jimenez, J
   Olmo, GJ
   Orazi, E
TI The trivial role of torsion in projective invariant theories of gravity with non-minimally coupled matter fields
SO Classical and Quantum Gravity
JI Class. Quantum Gravity
PY 2017
BP 235003 - 20pp
VL 34
IS 23
DI 10.1088/1361-6382/aa9151
LA English
DE modified gravity; metric-affine theories; torsion; non-minimal couplings
AB 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.
ER