Varying-Alpha Cosmologies with Potentials

TL;DR

This paper extends the BSBM model for varying fine structure constant by including scalar field potentials, analyzing their cosmological evolution, and constraining models with astronomical data.

Contribution

It introduces new scalar field potentials into the BSBM framework and derives general solutions for their evolution across cosmic eras.

Findings

Astronomical data tightly constrain the evolution of α from redshift 1 to 3.5.

Strong limits are placed on deviations of the potential from a cosmological constant.

The evolution of the scalar field depends mainly on either the potential or matter coupling, based on parameters.

Abstract

We generalize the Bekenstein-Sandvik-Barrow-Magueijo (BSBM) model for the variation of the fine structure 'constant', $\alpha ,$ to include an exponential or inverse power-law self-potential for the scalar field $% \phi $ which drives the time variation of $\alpha $, and consider the dynamics of $\phi$ in such models. We find solutions for the evolution of $\phi $ or $\alpha $ in matter-, radiation- and dark-energy-dominated cosmic eras. In general, the evolution of $\phi $ is well determined solely by either the self-potential or the coupling to matter, depending on the model parameters. The results are general and applicable to other models where the evolution of a scalar field is governed by a matter coupling and a self-potential. We find that the existing astronomical data stringently constrains the possible evolution of $\alpha $ between redshifts $z\simeq 1-3.5$ and the present, and this leads to very strong limit on the allowed deviation of the potential from that of a pure cosmological constant.