On relevance of modified gravities

TL;DR

This paper evaluates modified gravity theories, finding that those based on quadratic Riemann invariants are unsuitable due to inconsistencies or instabilities, and advocates for the frame field theory within Absolute Parallelism as a better alternative.

Contribution

It demonstrates the limitations of quadratic Riemann invariant-based gravities and promotes the frame field theory in Absolute Parallelism as a more consistent modification.

Findings

Quadratic Riemann invariant gravities are incompatible or unstable.

Frame field theory in Absolute Parallelism avoids singularities.

D=5 is essential for the frame field theory.

Abstract

It is shown that modified gravity theories with a Lagrangian composed of the three quadratic invariants of the Riemann curvature tensor are not appropriate. The field equations are either incompatible and/or irregular [like f(R)-gravities], or, if compatible, lead to the linear instability of polarizations relating to the Weyl tensor. A more relevant modification is the frame field theory, namely the best and unique variant of Absolute Parallelism; it has no free parameters (D=5 is a must) and no singularities arising in solutions. I sketch few remarkable features of this theory.