  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.
