On relevance of modified gravities

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.

Submitted to the Zelmanov Journal; 11 pages; improvements and new issues: (trivial) `weak' Lagrangian (term of N.Kh. Ibragimov) and classification of AP polarizations