Brans-Dicke theory of gravity with torsion: A possible solution of $\omega$-problem

We study the Brans-Dicke theory of gravity in Riemann-Cartan space-times and obtain general torsion solutions, which are completely determined by the Brans-Dicke scalar field $\Phi$, in the false- vacuum-energy–dominated epoch. The substitution of the torsion solutions back to our action gives the original Brans-Dicke action with $\Phi$-dependent Brans-Dicke parameter $\omega (\Phi )$. The evolution of $\omega (\Phi )$ during the inflation is studied and it is found that $\omega$ approaches infinity at the end of inflation. This may solve the $\omega$-problem in the extended inflation model.

Figure 1

Evolution of $a(T)$, $\chi (T)$ and $\omega$ during the inflation, where $T$ is a dimensionless time parameter normalized by $T\equiv {10}^{-2}{M}_{F}t$. (1) The top left panel indicates $\ln a-T$ diagram and the top right panel denotes $\chi (T)-T$ diagram. (2) The bottom left panel indicates the evolution of the velocity of $\chi$ and the bottom right panel shows the evolution of $\ln \omega$ with respect to $T$.