Behavior of varying-alpha cosmologies

Abstract

We determine the behaviour of a time-varying fine structure 'constant' α(t) during the early and late phases of universes dominated by the kinetic energy of changing α(t), radiation, dust, curvature, and lambda, respectively. We show that after leaving an initial vacuum-dominated phase during which α increases, α remains constant in universes like our own during the radiation era, and then increases slowly, proportional to a logarithm of cosmic time, during the dust era. If the universe becomes dominated by negative curvature or a positive cosmological constant then α tends rapidly to a constant value. The effect of an early period of de Sitter or power-law inflation is to drive α to a constant value. Various cosmological consequences of these results are discussed with reference to recent observational studies of the value of α from quasar absorption spectra and to the existence of life in expanding universes.

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“…Such a theory was first formulated by Bekenstein [19] as a generalisation of Maxwell's equations but ignoring the consequences for the gravitational field equations. Recently, Magueijo, Sandvik and myself have completed this theory [22,21,20,24] to include the coupling to the gravitational sector and analysed its general cosmological consequences. This theory considers only a variation of the electromagnetic coupling and so far ignores any unification with the strong and electroweak interactions.…”

“…(22). This is parametrised by ζ ≡ L em /ρ, where ρ is the energy density, and for baryonic matter L em = E 2 /2.…”

“…[22,21,20,24], [35]. Typically, the variation in α does not have a significant effect on the evolution of the scale factor at late times although the cosmological expansion does significantly affect the evolution of α.…”

“…Our generalisation of the scalar theory proposed by Bekenstein [19] described in ref. [22,21,20,24] includes the gravitational effects of ψ and gives the field equations:…”

“…Since the observational data is consistent with a smaller value of α in the past, we will in this paper confine our study to negative values of ζ m , in line with our recent discussion in Refs. [22,21,20,24]. The conservation equations for the non-interacting radiation and matter densities arė…”