  Dilatons (and moduli) couple to the masses and coupling constants of ordinary
matter, and these quantities are fixed by the local value of the dilaton field.
If, in addition, the dilaton with mass $m_\phi$ contributes to the cosmic dark
matter density, then such quantities oscillate in time at the dilaton Compton
frequency. We show how these oscillations lead to broadening and shifting of
the Voigt profile of the Ly$\alpha$ forest, in a manner that is correlated with
the local dark matter density. We further show how tomographic methods allow
the effect to be reconstructed by observing the Ly$\alpha$ forest spectrum of
distant quasars. We then simulate a large number of quasar lines of sight using
the lognormal density field, and forecast the ability of future astronomical
surveys to measure this effect. We find that in the ultra low mass range
$10^{-32}\text{ eV}\leq m_\phi\leq 10^{-28}\text{ eV}$ upcoming observations
can improve over existing limits to the dilaton electron mass and fine
structure constant couplings set by fifth force searches by up to five orders
of magnitude. Our projected limits apply assuming that the ultralight dilaton
makes up a few percent of the dark matter density, consistent with upper limits
set by the cosmic microwave background anisotropies.
