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

TL;DR

This paper investigates how $f(R)$ gravity theories can be constrained by observational limits on the time variation of the fine structure constant, linking fundamental physics with cosmological data.

Contribution

It introduces a method to use observational bounds on the fine structure constant's variation to constrain $f(R)$ gravity models.

Findings

Time variation of fine structure constant can restrict $f(R)$ models.

Conformal coupling in $f(R)$ theories affects fundamental constants.

Observational bounds provide a new criterion for model viability.

Abstract

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. We will use observational bounds on these variations and argue that it provides a criterion for constraining $f(R)$ models.