We present predictions of the correlation between the Ly \alpha forest absorption in quasar spectra and the mass within \sim 5 h ^ { -1 } { Mpc } ( comoving ) of the line of sight , using fully hydrodynamic and hydro-PM numerical simulations of the cold dark matter model supported by present observations .
The observed correlation based on galaxies and the Ly \alpha forest can be directly compared to our theoretical results , assuming that galaxies are linearly biased on large scales .
Specifically , we predict the average value of the mass fluctuation , < \delta _ { m } > , conditioned to a fixed value of the Ly \alpha forest transmitted flux \delta _ { F } , after they have been smoothed over a 10 h ^ { -1 } { Mpc } cube and line of sight interval , respectively .
We find that < \delta _ { m } > / \sigma _ { m } as a function of \delta _ { F } / \sigma _ { F } has a slope of 0.6 at this smoothing scale , where \sigma _ { m } and \sigma _ { F } are the rms dispersions ( this slope should decrease with the smoothing scale ) .
We show that this value is largely insensitive to the cosmological model and other Ly \alpha forest parameters .
Comparison of our predictions to observations should provide a fundamental test of our ideas on the nature of the Ly \alpha forest and the distribution of galaxies , and can yield a measurement of the bias factor of any type of galaxies that are observed in the vicinity of Ly \alpha forest lines of sight .