We discuss the feasibility of measuring the cosmological geometry using the redshift space correlation function of the Ly \alpha forest in multiple lines of sight , as a function of angular and velocity separation .
The geometric parameter that is measured is f ( z ) \equiv c ^ { -1 } H ( z ) D ( z ) , where H ( z ) is the Hubble constant and D ( z ) the angular diameter distance at redshift z .
The correlation function is computed in linear theory .
We describe a method to measure it from observations with the Gaussianization procedure of Croft et al .
( 1998 ) to map the observed Ly \alpha forest transmitted flux to an approximation of the linear density field .
The effect of peculiar velocities on the shape of the recovered power spectrum is pointed out .
We estimate the error in recovering the f ( z ) factor from observations due to the variance in the Ly \alpha absorbers .
We show that \sim 20 pairs of quasars ( separations < 3 ^ { \prime } ) are needed to distinguish a flat \Omega _ { 0 } = 1 universe from a universe with \Omega _ { 0 } = 0.2 , \Omega _ { \Lambda } = 0.8 .
A second parameter that is obtained from the correlation function of the Ly \alpha forest is \beta \simeq \Omega ( z ) ^ { 0.6 } / b ( affecting the magnitude of the peculiar velocities ) , where b is a linear theory bias of the Ly \alpha forest .
The statistical error of f ( z ) can be reduced if b can be determined independently from numerical simulations , reducing the number of quasar pairs needed for constraining cosmology to approximately six .
On small scales , where the correlation function is higher , f ( z ) should be measurable with fewer quasars , but non-linear effects must then be taken into account .
The anisotropy of the non-linear redshift space correlation function as a function of scale should also provide a precise quantitative test of the gravitational instability theory of the Ly \alpha forest .