[en] We obtain the equation that describe the conditions of quantization for neutral massless bosons on an arbitrary curved space-time, obtained using a particular theoretical formalism developed in a previous work (M.R.A. Arcodıa and M. Bellini, arXiv:1703.01355). In particular, we study the emission of neutral massless spin-(1, 2)ℏ bosons during pre-inflation using the recently introduced unified spinor field theory. We conclude that during pre-inflation (which is governed by vacuum equation of state), gravitational radiation is emitted, which could be detected in the future, as primordial gravitational radiation.