  We discuss the feasibility of measuring the cosmological metric using the
redshift space correlation function of the Lya forest in multiple lines of
sight, as a function of angular and velocity separation. The geometric
parameter that is measured is f(z) = H(z) D(z)/c, 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 Lya 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 Lya absorbers. We show that ~ 20
pairs of quasars (separations < 3') 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 Lya 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 Lya forest. The statistical
error of f(z) is 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 Lya forest.
