  Recent observations of Gravitational Waves (GW) generated by black-hole
collisions have opened a new window to explore the universe in diverse scales.
Detection of primordial gravitational waves is expected to happen in the next
years. However, the standard theory to describe these effects was developed for
weak gravitational waves, when their dynamics can be linearized. In this work
we develop a non-perturbative formalism to describe GW using the Unified Spinor
Fields (USF) theory. The tensor index is calculated and we obtain that it must
be $0.0283 <n_T < 0.0407$, in order for the $+$ and $\times$ polarisations
modes to have the same spectrum. This imposes some restriction on the constant
of self-interaction $3.0018\,<\,\xi^2\,< \,3.0025$ of the fermionic source. The
most relevant result here obtained is that the intensity of energy density for
GW during inflation is $1.25\times 10^{-4} \left(\frac{m}{H}\right)^2 \, <
\,\Omega_{GW} \, < \,1.75\times 10^{-4} \left(\frac{m}{H}\right)^2$, where $m$
is the mass of the $1/2$-spin fermionic fields and $H$ the Hubble parameter
during inflation. This cut imposes restrictions on the mass of these fields:
$\left({m\over H}\right)^2\lesssim 1.1\,h_0^2\times 10^{-11}$.
