Cosmology beyond BAO from the 3D distribution of the Lyman-α forest

Abstract

We propose a new method for fitting the full-shape of the Lyman-α (Ly α) forest 3D correlation function in order to measure the Alcock-Paczynski (AP) effect. Our method preserves the robustness of baryon acoustic oscillations (BAO) analyses, while also providing extra cosmological information from a broader range of scales. We compute idealized forecasts for the Dark Energy Spectroscopic Instrument (DESI) using the Ly α autocorrelation and its cross-correlation with quasars, and show how this type of analysis improves cosmological constraints. The DESI Ly α BAO analysis is expected to measure H(zeff)rd and DM(zeff)/rd with a precision of ∼ 0.9 per cent, where H is the Hubble parameter, rd is the comoving BAO scale, DM is the comoving angular diameter distance, and the effective redshift of the measurement is zeff 2.3. By fitting the AP parameter from the full shape of the two correlations, we show that we can obtain a precision of ∼ 0.5-0.6 per cent on each of H(zeff)rd and DM(zeff)/rd. Furthermore, we show that a joint full-shape analysis of the Ly α auto and cross-correlation with quasars can measure the linear growth rate times the amplitude of matter fluctuations in spheres of 8 h-1Mpc, fσ8(zeff). Such an analysis could provide the first ever measurement of fσ8(zeff) at redshift zeff > 2. By combining this with the quasar autocorrelation in a joint analysis of the three high-redshift two-point correlation functions, we show that DESI could be able to measure fσ8(zeff 2.3) with a precision of 5-12 per cent, depending on the smallest scale fitted.