Constraining $f(R)$ Theories with Temporal Variation of Fine Structure Constant

Understand

It is well-known that $f(R)$ theories in Einstein frame is conformally equivalent to quintessence models in which the scalar field minimally couples with gravity.

• If there exists a matter system in Jordan frame, then it interacts with the scalar field in Einstein frame due to the conformal transformations.
• This interaction, in general, may lead to changes of fundamental constants.
• Here we will consider possible time variation of fine structure constant in a general $f(R)$ theory.