  We investigate the quantum origin of the primordial cosmological
gravitational waves in the Brans-Dicke theory in the two conformally related
frames, the Jordan-Brans-Dicke frame and the Einstein frame. We calculated the
theoretical observable in both frames and we compared both with General
Relativity. We compute the number of gravitons $N_k$ produced during inflation
and the observables: power spectrum $P_T$, spectral index $n_T$ and energy
density $\Omega_k$. The comparison shows that for the case of the particles
number $N_k$ the results are the same in both frames and in General Relativity
when the Brans-Dicke parameter is much bigger than unity. For the spectral
index $n_T$ we show that it is possible to get a scale invariant perturbation
in the Jordan-Brans-Dicke frame when $\omega\rightarrow\infty$ and in the
Einstein frame when $\omega\rightarrow\pm\infty$. In both frames, the results
found for the power spectrum $P_T$ and the energy density $\Omega$ show that
the prefered values of $\omega$ are diferente from that that are found in the
local tests.
