Elements of the Metric-Affine gravity I: Aspects of F(R) theories reductions and the topologically massive gravity

Some classical aspects of Metric-Affine Gravity are reviewed in the context of the F-(n)(R) type models (polynomials of degree n in the Riemann tensor) and the topologically massive gravity. At the nonperturbative level, we explore the consistency of the field equations when the F-(n) (R) models are reduced to a Riemann-Christoffel (RCh) space-time, either via a Riemann-Cartan (RC) space or via an Einstein-Weyl (EW) space. It is well known for the case F-(1) (R) = R that any path or reduction classes via RC or EW leads to the same field equations with the exception of the F-(n) (R) theories for n > 1. We verify that this discrepancy can be solved by imposing nonmetricity and torsion constraints. In particular, we explore the case F-(2) (R) for the interest in expected physical solutions as those of conformally flat class. On the other hand, the symmetries of the topologically massive gravity are reviewed, as the physical content in RC and EW scenarios. The appearance of a nonlinearly modified selfdual model in RC and existence of many nonunitary degrees of freedom in EW with the suggestion of a modified model for a massive gravity which cure the unphysical propagations shall be discussed.

Automated summary

The paper reviews classical aspects of Metric-Affine Gravity in the context of F-(n)(R) type models and topologically massive gravity, exploring the consistency of field equations at the nonperturbative level. It is found that discrepancies in field equations for F-(n)(R) theories can be solved by imposing nonmetricity and torsion constraints. This discrepancy is particularly evident for F-(2)(R) models, emphasizing the importance of these constraints for resolving physical solutions.