  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\cite{MM}. In
particular, we study the emission of neutral massless $(1, 2)\hbar$-spin bosons
during pre-inflation using the recently introduced unified spinor field theory.
We conclude that during pre-inflation (which is governed by an vacuum equation
of state), is emitted gravitational radiation, which could be detected in the
future, as primordial gravitational radiation.
