Abstract
We measure the expansion rate of the Universe at redshift $z=2.3$ from the
anisotropy of Lyman-$\alpha$ (Ly$\alpha$) forest correlations measured by the
Sloan Digital Sky Survey (SDSS). Our result is the most precise from
large-scale structure at $z>1$. In flat $Łambda$CDM we determine the matter
density to be $Ømega_m=0.36^+0.03_-0.04$ from Ly$\alpha$ alone, a
factor of two tighter than baryon acoustic oscillation results from the same
data. Using a nucleosynthesis prior, we measure the Hubble constant to be
$H_0=63.2\pm2.5$ km/s/Mpc. In combination with other SDSS tracers, we find
$H_0=67.2\pm0.9$ km/s/Mpc and measure the dark energy equation-of-state
parameter to be $w=-0.90\pm0.12$. Our work opens a new avenue for constraining
cosmology at high redshift.
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