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

Cosmological variation of the fine structure constant alpha due to the evolution of a spatially homogeneous ultralight scalar field (msimilar toH(0)) during the matter and Lambda dominated eras is analyzed. Agreement of Deltaalpha/alpha 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 alpha(t) in this model goes to a constant value (alpha) over bar approximate toalpha(0) in the early radiation and the late Lambda dominated eras. The coupling of the scalar field to (nonrelativistic) matter drives alpha slightly away from (alpha) over bar in the epochs when the density of matter is important. Simultaneous agreement with the more restrictive bounds on the variation \Deltaalpha/alpha\ 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-Lambda, where H-Lambda=Omega(Lambda)(1/2)H(0). Depending on the scalar field mass, alpha may be slightly smaller or larger than alpha(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 alpha 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 (alpha/alpha)(0).