Time variation of the proton-electron mass ratio and the fine structure constant with a runaway dilaton

Recent astrophysical observations indicate that the proton-electron mass ratio and the fine structure constant have gone through nontrivial time evolution. We discuss their time variation in the context of a dilaton runaway scenario with gauge coupling unification at the string scale $M_{\mathrm{s}}$. We show that the choice of adjustable parameters allows them to fit the same order magnitude of both variations and their (opposite) signs in such a scenario.

Figure 1

The time evolution of $\mu$ and $\alpha$ (solid curve) in runaway dilaton scenario. The upper panel is $\mu$ determined from the spectral lines of hydrogen molecules. The data are taken from 6. The lower panel is $\alpha$ determined from quasar absorption lines at several redshifts. Open circles are the binned data from 2 (in each bin the value of $\Delta \alpha /\alpha$ is the weighted mean), crosses are from 4 and filled circles are from [5]. The datum at $z\simeq 0.16$, 0.44 is the Oklo bound [19] and the ${}^{187}\mathrm{Re}$ bound [20], respectively.