We study the evolution with redshift, from z similar to 5 to z = 0, of
the Lyman alpha forest in a CDM model using numerical simulations inc
luding collisionless particles only. The baryonic component is assumed
to follow the dark matter distribution. We distinguish between two po
pulations of particles: Population P-s traces the filamentary structur
es of the dark matter, evolves slowly with redshift and, for N(HI) gre
ater than or similar to 10(14) cm(-2), dominates the number density of
lines at z < 3; most of population P-u is located in underdense regio
ns and for the same column densities, disappears rapidly at high redsh
ift. We generate synthetic spectra from the simulation and show that t
he redshift evolution of the Lyman alpha forest (decrement, N(HI) dist
ribution) is well reproduced over the whole redshift range for Omega(b
)h(2) similar to 0.0125 and J(-21) approximate to 0.1 at z similar to
3 where J(-21) is the UV background flux intensity in units of 10(-21)
erg cm(-2) s(-1) Hz(-1) sr(-1). The total number of lines with N(HI)
greater than or similar to 10(12) cm(-2) remains approximately constan
t from z similar to 4 to z = 1. At z similar to 0, the number density
of lines per unit redshift with log N(HI) > 12, 13, 14 is of the order
of 400, 100, and 20 respectively. Therefore, at low redshift, if most
of the strong (w(r) > 0.3 Angstrom) lines are expected to be associat
ed with galaxies, the bulk of the Lyman alpha forest however should ha
ve lower equivalent width and should not be tightly correlated with ga
laxies.