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 & Paczyński in 1979, using observations of the Lyα 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~2-4. Since this relationship depends on the parameters of the cosmological model, these parameters may be determined using the Lyα forest. While this test is relatively insensitive to the density parameter Ω_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 Λ) and its equation of state. With only 25 pairs of quasar spectra at angular separations 05-2', one can discriminate between an Ω=0.3 open universe (Λ=0) and an Ω=0.3 flat (Λ-dominated) universe at the 4 σ level.