  A viable quantum theory does not allow curvature invariant terms of different
higher orders to be accommodated in the gravitational action. We show that
there is indeed a conflict between the curvature squared and Gauss-Bonnet
squared terms from the point of view of hermiticity. This means one should
choose either, in addition to the Einstein-Hilbert term, but never the two
together. We explore early cosmic evolution with Gauss-Bonnet squared term.
