Constraints on the Cosmic Expansion Rate at Redshift 2.3 from the Lyman-α Forest

We determine the product of the expansion rate and angular-diameter distance at redshift z =2.3 from the anisotropy of Lyman-α (Ly α ) forest correlations measured by the Sloan Digital Sky Survey (SDSS). Our result is the most precise from large-scale structure at z >1 . Using the flat Λ cold dark matter model we determine the matter density to be Ω_m=0.3 6_-0.04^+0.03 from Ly α alone. This is a factor of 2 tighter than baryon acoustic oscillation results from the same data due to our use of a wide range of scales (25 <r <180 h^-1 Mpc ). Using a nucleosynthesis prior, we measure the Hubble constant to be H₀=63.2 ±2.5 km /s /Mpc . In combination with other SDSS tracers, we find H₀=67.2 ±0.9 km /s /Mpc and measure the dark energy equation-of-state parameter to be w =-0.90 ±0.12 . Our Letter opens a new avenue for constraining cosmology at high redshift.