Cosmological variation of the fine structure constant from an ultralight scalar field: The effects of mass

Cosmological variation of the fine structure constant α due to the evolution of a spatially homogeneous ultralight scalar field (m∼H₀) 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 α̅ ≈α₀ in the early radiation and the late Λ dominated eras. The coupling of the scalar field to (nonrelativistic) matter drives α slightly away from α̅ 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^1/2H₀. Depending on the scalar field mass, α may be slightly smaller or larger than α₀ 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 (α̇/α)₀.