Measuring the Cosmological Geometry from the Lyα Forest along Parallel Lines of Sight

Abstract

The possibility of measuring the cosmological geometry using the redshift space correlation function of the Lyα forest in multiple lines of sight as a function of angular and velocity separation is discussed. The geometric parameter to be measured is f(z)≡c-1H(z)DA(z), where H(z) is the Hubble constant and DA(z) the angular diameter distance at redshift z. The correlation function is computed in linear theory, assuming that the Lyα forest is a result of gravitational instability in a photoionized intergalactic medium. We describe a method to measure the correlation from observations with the Gaussianization procedure of Croft et al. to map the observed Lyα 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 Lyα absorbers. We show that at least ~25 pairs of quasars (separations <3') are needed to distinguish a flat Ω0=1 universe from a universe with Ω0=0.2, ΩΛ=0.8. A second parameter that is obtained from the correlation function of the Lyα forest is βΩ(z)0.6/b (affecting the magnitude of the peculiar velocities), where b is a linear theory bias of the Lyα forest. In the theory of the Lyα forest assumed here, the parameter β can be predicted from numerical simulations; once β is known, the number of quasar pairs needed to constrain f is reduced to about six. On small scales, where the correlation function is higher, f(z) should be measurable with fewer quasars, but nonlinear effects must then be taken into account. The anisotropy of the nonlinear redshift space correlation function as a function of scale should also provide a precise quantitative test of the gravitational instability theory of the Lyα forest.