Observational constraints of the gravitational waves in the Brans-Dicke theory: Einstein frame and Jordan-Brans-Dicke frame

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 Nk produced during inflation and the observables: power spectrum PT, spectral index nT and energy density Ωk. The comparison shows that for the case of the particles number Nk 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 nT we show that it is possible to get a scale invariant perturbation in the Jordan-Brans-Dicke frame when ω→∞ and in the Einstein frame when ω→±∞. In both frames, the results found for the power spectrum PT and the energy density Ω show that the preferred values of ω are different from that are found in the local tests.