Observational constraints of the Gravitational Waves in the Brans-Dicke Theory

We investigate the quantum origin of the primordial cosmological gravitational waves in the Brans-Dicke theory. 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 ${\mathrm{\Omega }}_k$. By comparison with General Relativity we see that the results for both theories are the same for the case of the particles number $N_k$ and for the case of the power spectrum $P_T$ and the energy density $\mathrm{\Omega }$ only when $\omega <10$. For the spectral index $n_T$ we found that when the Brans-Dicke coupling parameter $\omega$ is bigger than unity the spectral index approximates the expression found in the General Relativity. This may awake us to the possibility that $\omega$ varies with the cosmological scale.