Local Varying-Alpha Theories

TL;DR

This paper develops a Lorentz-invariant theory of local varying alpha using dielectric analogies, leading to new cosmological models with early universe phenomena like bounces and inflation.

Contribution

It introduces a novel formalism for local alpha variation based on algebraic relations, extending previous Klein-Gordon models and exploring their cosmological implications.

Findings

Classical self-energy divergence can be mitigated.

New cosmological solutions include bounce and inflation scenarios.

Early universe variations in alpha can induce diverse expansion behaviors.

Abstract

In a recent paper we demonstrated how the simplest model for varying alpha may be interpreted as the effect of a dielectric material, generalized to be consistent with Lorentz invariance. Unlike normal dielectrics, such a medium cannot change the speed of light, and its dynamics obey a Klein-Gordon equation. This work immediately suggests an extension of the standard theory, even if we require compliance with Lorentz invariance. Instead of a wave equation, the dynamics may satisfy a local algebraic relation involving the permittivity and the properties of the electromagnetic field, in analogy with more conventional dielectric (but still preserving Lorentz invariance). We develop the formalism for such theories and investigate some phenomenological implications. The problem of the divergence of the classical self-energy can be solved, or at least softened, in this framework. Some interesting new cosmological solutions for the very early universe are found, including the possibility of a bounce, inflation and expansion with a loitering phase, all of which are induced by early variations in alpha.