  The concept of early Universe inflation resolves several problems of hot Big
Bang theory and quantitatively explains the origin of the inhomogeneities in
the present Universe. However, it is not possible to arrange inflation in a
scalar field model with renormalizable potential, such that it would not
contradict the recent Planck data. For this reason, inflaton must have also
higher derivative couplings suppressed at least by the Planck scale. We show
that these couplings may be relevant during reheating and lead to
non-negligible production of gravitons. We consider the possibility that the
unitarity breaking scale for the model of inflation is lower than the Planck
scale and compute production of gravitons during reheating, due to the inflaton
decay to two gravitons and graviton bremsstrahlung process. The spectrum of
produced gravitons is crucially dependent on reheating temperature and inflaton
mass. We find that for low reheating temperature decay to gravitons lead to
significant amount of dark radiation. Confronting this result with CMB
constraints, we find reheating dependent bounds on the unitarity breaking
scale. We also compare the obtained gravitational wave signals with the
projected limits of future high frequency gravitational wave experiments.
