Cosmological Variation of the Fine Structure Constant from an Ultra-Light Scalar Field: The Effects of Mass

Abstract

Cosmological variation of the fine structure constant $α$ due to the evolution of a spatially homogeneous ultra-light scalar field ($m \sim H_0$) during the matter and $Λ$ dominated eras is analyzed. Agreement of $Δα/α$ with the value suggested by recent observations of quasar absorption lines is obtained by adjusting a single parameter, the coupling of the scalar field to matter. Asymptotically $α(t)$ in this model goes to a constant value $\barα \approx α_0$ in the early radiation and the late $Λ$ dominated eras. The coupling of the scalar field to (nonrelativistic) matter drives $α$ slightly away from $\barα$ in the epochs when the density of matter is important. Simultaneous agreement with the more restrictive bounds on the variation $|Δα/α|$ from the Oklo natural fission reactor and from meteorite samples can be achieved if the mass of the scalar field is on the order of 0.5--0.6 $H_Λ$, where $H_Λ= Ω_Λ^{1/2} H_0$. Depending on the scalar field mass, $α$ may be slightly smaller or larger than $α_0$ at the times of big bang nucleosynthesis, the emission of the cosmic microwave background, the formation of early solar system meteorites, and the Oklo reactor. The effects on the evolution of $α$ due to nonzero mass for the scalar field are emphasized. An order of magnitude improvement in the laboratory technique could lead to a detection of $(\dotα/α)_0$.