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 ( \Lambda CDM ) 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 .