  Noether symmetry of F(R) theory of gravity in vacuum or in matter dominated
era yields three-half power law of R. We show that this particular curvature
invariant term is very special in the context of isotropic and homogeneous
cosmological model as it makes the first fundamental form cyclic. As a result,
it allows a unique power law solution, typical for this particular fourth order
theory of gravity, both in the vacuum and in the matter dominated era. This
power law solution has been found to be quite good to explain the early stage
but not so special and useful to explain the late stage of cosmological
evolution. The usefulness of Palatini variational technique in this regard has
also been discussed.
