We present a model for the Lyman- \alpha absorbers that treats all objects ( from the low-density forest clouds to the dense damped systems ) in a unified description .
This approach is consistent with an earlier model of galaxies ( luminosity function , metallicity ) but also with the known description of the density field in the small-scale non-linear regime .
We consider two cosmological models : a critical universe \Omega = 1 with a CDM power-spectrum , and an open CDM universe with \Omega _ { 0 } = 0.3 , \Lambda = 0 .
We reproduce the available data on column density distribution as a function of redshift , the value of the main new parameter , the background ionizing UV flux , being consistent with the observed limits .
This allows a quantitatively trustable analytical description of the opacity , mass , size , velocity dispersion and metallicity of these absorbers , over a range of column densities spanning 10 orders of magnitude .
Moreover , together with an earlier model of galaxy formation this draws a unified picture of the redshift evolution of structures in the universe , from underdense clouds to massive high density galaxies , from weak to very deep potential wells .