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 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 -> infinity and in the Einstein frame when omega -> +/-infinity. In both frames, the results found for the power spectrum P-T and the energy density Omega show that the preferred values of omega are different from that are found in the local tests. (C) 2012 Published by Elsevier B.V.