Oscillating scalar fields in extended quintessence

Understand

We study a rapidly-oscillating scalar field with potential $V(\phi) = k|\phi|^n$ nonminally coupled to the Ricci scalar $R$ via a term of the form $(1- 8 \pi G_0 \xi \phi^2) R$ in the action.

• In the weak coupling limit, we calculate the effect of the nonminimal coupling on the time-averaged equation of state parameter $\gamma = (p + \rho)/\rho$.
• The change in $\langle \gamma \rangle$ is always negative for $n \ge 2$ and always positive for $n < 0.71$ (which includes the case where the oscillating scalar field could serve as dark energy), while it can be either positive or negative for intermediate values of $n$.
• Constraints on the time-variation of $G$ force this change to be infinitesimally small at the present time whenever the scalar field dominates the expansion, but constraints in the early universe are not as stringent.