A Generalized Theory of Varying Alpha

TL;DR

This paper generalizes the BSBM theory of varying alpha by allowing the coupling constant to depend on the scalar field, analyzing late-time cosmological behaviors, and comparing models with astronomical data.

Contribution

It introduces a generalized model where the coupling constant varies with the scalar field, exploring its implications for cosmology and observational constraints.

Findings

Conditions for increasing alpha over time.

Conditions for decreasing alpha over time.

Compatibility with quasar absorption spectra data.

Abstract

In this paper, we formulate a generalization of the simple Bekenstein-Sandvik-Barrow-Magueijo (BSBM) theory of varying alpha by allowing the coupling constant, \omega, for the corresponding scalar field \psi\ to depend on \psi. We focus on the situation where \omega\ is exponential in \psi\ and find the late-time behaviours that occur in matter-dominated and dark-energy dominated cosmologies. We also consider the situation when the background expansion scale factor of the universe evolves in proportion to an arbitrary power of the cosmic time. We find the conditions under which the fine structure `constant' increases with time, as in the BSBM theory, and establish a cosmic no-hair behaviour for accelerating universes. We also find the conditions under which the fine structure `constant' can decrease with time and compare the whole family of models with astronomical data from quasar absorption spectra.