A geometrical test of the cosmological energy contents using the Lyα forest

We explore a version of the test of cosmological geometry proposed by Alcock & Paczynski in 1979, using observations of the Ly alpha forest in the spectra of close quasar pairs. By comparing the correlations in absorption in one quasar spectrum with correlations between the spectra of neighboring quasars, one can determine the relation of the redshift distance scale to the angle distance scale at the redshift of the absorbers, z similar to 2-4. Since this relationship depends on the parameters of the cosmological model, these parameters may be determined using the Ly alpha forest. While this test is relatively insensitive to the density parameter Omega(m) in a dust-dominated universe, it is more sensitive to the presence of a matter component with large negative pressure (such as a cosmological constant Lambda) and its equation of state. With only 25 pairs of quasar spectra at angular separations 0.'5-2', one can discriminate between an Omega(m) = 0.3 open universe (Lambda = 0) and an Omega(m) = 0.3 flat (Lambda-dominated) universe at the 4 sigma level.