On Generalized Theories of Varying Fine Structure Constant

TL;DR

This paper explores a scalar-tensor theory of gravity that explains cosmic acceleration and allows for a mild variation of the fine structure constant, fitting observational data and analyzing implications for cosmic history.

Contribution

It introduces a generalized scalar field model that links variations in the fine structure constant with cosmic acceleration, extending previous theories with new couplings and formalism.

Findings

The model fits observational data within current constraints.

The scalar field's coupling affects the variation of $eta$ and $G$ over cosmic time.

Different coupling schemes produce distinct cosmic evolution patterns.

Abstract

We work with a class of scalar extended theory of gravity that can drive the present cosmic acceleration as well as accommodate a mild cosmic variation of the fine structure constant $\alpha$. The motivation comes from a vintage theory developed by Bekenstein, Sandvik, Barrow and Magueijo. The $\alpha$ variation is introduced by a real scalar field interacting with charged matter. We execute a cosmological reconstruction based on a parametrization of the present matter density of the Universe. Observational consistency is ensured by comparing the theoretical estimates with JLA + OHD + BAO data sets, using a Markov chain Monte Carlo simulation. An analysis of molecular absorption lines from HIRES and UVES spectrographs is considered as a reference for the variation of $\alpha$ at different redshifts. Two examples are discussed. The first explores a field-dependent kinetic coupling of the scalar field interacting with charged matter. The second example is a generalized Brans-Dicke formalism where the varying $\alpha$ is fitted in as an effective matter field. This generates a simultaneous variation of the Newtonian constant $G$ and $\alpha$. The pattern of this variation can have a crucial role in cosmic expansion history.