  It is known that the perturbative instability of tensor excitations in higher
derivative gravity may not take place if the initial frequency of the
gravitational waves are below the Planck threshold. One can assume that this is
a natural requirement if the cosmological background is sufficiently mild,
since in this case the situation is qualitatively close to the free
gravitational wave in flat space. Here, we explore the opposite situation and
consider the effect of a very far from Minkowski radiation-dominated or de
Sitter cosmological background with a large Hubble rate, e.g., typical of an
inflationary period. It turns out that, then, for initial Planckian or even
trans-Planckian frequencies, the instability is rapidly suppressed by the very
fast expansion of the universe.
