On $f(R)$ gravity in scalar-tensor theories

Understand

We study $f(R)$ gravity models in the language of scalar-tensor theories.

• The correspondence between $f(R)$ gravity and scalar-tensor theories is revisited since $f(R)$ gravity is a subclass of Brans-Dicke models, with a vanishing coupling constant ($\omega=0$).
• In this treatment, four $f(R)$ toy models are used to analyze the early-universe cosmology, when the scalar field $\phi$ dominates over standard matter.
• We have obtained solutions to the Klein-Gordon equation for those models.