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.
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