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

TL;DR

This paper compares the predictions of primordial gravitational waves in Brans-Dicke theory across two conformally related frames, analyzing observable quantities and their consistency with General Relativity and experimental constraints.

Contribution

It provides a detailed comparison of gravitational wave observables in Jordan-Brans-Dicke and Einstein frames, highlighting conditions for scale invariance and deviations from local tests.

Findings

Number of gravitons $N_k$ is consistent in both frames and with General Relativity for large Brans-Dicke parameter.

Scale invariance of the spectral index $n_T$ is achievable in both frames as $ ightarrow ightarrowty$.

Preferred values of $oldsymbol{oldsymbol{oldsymbol{ ext{omega}}}}$ differ from local experimental bounds.

Abstract

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.