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

TL;DR

This paper explores a modified Brans-Dicke gravity model incorporating torsion in Riemann-Cartan spacetime, deriving solutions that suggest a dynamic evolution of the Brans-Dicke parameter, potentially resolving the $$-problem in inflationary cosmology.

Contribution

It introduces torsion into Brans-Dicke theory, deriving scalar-dependent solutions that lead to a variable , and shows  approaches infinity post-inflation, addressing the -problem.

Findings

 approaches infinity after inflation

Torsion solutions are determined by the scalar field 

The model provides a potential resolution to the -problem

Abstract

We study the Brans-Dicke theory of gravity in Riemann-Cartan space-times, and obtain general torsion solutions, which are completely determined by 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 to infinity at the end of inflation. This may solve the $\omega$-problem in the extended inflation model.