Precision cosmology from the Lyman α forest:: power spectrum and bispectrum

We investigate the promise of the Lyalpha forest for high-precision cosmology in the era of the Sloan Digital Sky Survey using low-order N-point statistics. We show that, with the existing data, one can determine the amplitude, slope and curvature of the slope of the matter power spectrum with a few per cent precision. Higher-order statistics such as the bispectrum provide independent information that can confirm and improve upon the statistical precision from the power spectrum alone. The achievable precision is comparable to that from the cosmic microwave background with upcoming satellites, and complements it by measuring the power spectrum amplitude and shape at smaller scales. Since the data cover the redshift range 2 < z < 4, one can also extract the evolution of the growth factor and Hubble parameter over this range, and provide useful constraints on the presence of dark energy at z > 2.