Time evolution of the fine structure constant in a two-field quintessence model

We examine the variation of the fine structure constant in the context of a two-field quintessence model. We find that, for solutions that lead to a transient late period of accelerated expansion, it is possible to fit the data arising from quasar spectra and comply with the bounds on the variation of $\alpha$ from the Oklo reactor, meteorite analysis, atomic clock measurements, cosmic microwave background radiation, and big bang nucleosynthesis. That is more difficult if we consider solutions corresponding to a late period of permanent accelerated expansion.

Figure 1

Evolution of $\alpha$ for a transient acceleration model with ${\zeta }_1=2\times {10}^{-6}$ and ${\zeta }_2=8\times {10}^{-5}$. In the upper panel, the boxes represent the QSO bounds given in Eq. (2) (top box), Eq. (3) (middle box), and Eq. (1) (lower box). Also shown is the QSO absorption systems data set of Chand et al. (Table 3 of Ref. [13]). The lower panel details the behavior of $\alpha$ for small values of $z$. The lower left plot shows the Oklo bound (dash-dotted lines) and the right one the meteorite bounds (dash-dotted and dotted lines correspond to $1\sigma$ and $2\sigma$, respectively).

Figure 2

Same as for Fig. 1 but for a permanent acceleration model with ${\zeta }_1=-4\times {10}^{-5}$ and ${\zeta }_2=1\times {10}^{-6}$.