  In quintessence models, the dark energy content of the universe is described
by a slowly rolling scalar field whose pressure and energy density obey an
equation of state of the form p=w $\rho$; w is in general a function of time
such that w<-1/3, in order to drive the observed acceleration of the Universe
today. The cosmological constant model LCDM corresponds to the limiting case
w=-1. In this paper, we explore the prospects of using the Lyman-alpha forest
to constrain w, using semi-analytical techniques to model the intergalactic
medium (IGM). A different value of w changes both the growth factor and the
Hubble parameter as a function of time. The resulting change in the optical
depth distribution affects the optical depth power spectrum, the number of
regions of high transmission per unit redshift and the cross-correlation
coefficient of spectra of quasar pairs. These can be detected in current data,
provided we have independent estimates of the thermal state of the IGM, its
ionization parameter and the baryon density.
