Cosmology beyond BAO from the 3D distribution of the Lyman-$\alpha$ forest

Abstract

We propose a new method for fitting the full-shape of the Lyman-$\alpha$ (Ly$\alpha$) forest three-dimensional (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$\alpha$ auto-correlation and its cross-correlation with quasars, and show how this type of analysis improves cosmological constraints. The DESI Ly$\alpha$ BAO analysis is expected to measure $H(z_{\mathrm{eff}})r_{\mathrm{d}}$ and $D_{\mathrm{M}}(z_{\mathrm{eff}})/r_{\mathrm{d}}$ with a precision of $\sim 0.9\%$ each, where $H$ is the Hubble parameter, $r_{\mathrm{d}}$ is the comoving BAO scale, $D_{\mathrm{M}}$ is the comoving angular diameter distance and the effective redshift of the measurement is $z_{\mathrm{eff}}\simeq 2.3$. By fitting the AP parameter from the full shape of the two correlations, we show that we can obtain a precision of $\sim 0.5-0.6\%$ on each of $H(z_{\mathrm{eff}})r_{\mathrm{d}}$ and $D_{\mathrm{M}}(z_{\mathrm{eff}})/r_{\mathrm{d}}$. Furthermore, we show that a joint full-shape analysis of the Ly$\alpha$ auto-correlation and its cross-correlation with quasars can measure the linear growth rate times the amplitude of matter fluctuations in spheres of $8h^{-1}$Mpc, $f{\sigma }_8(z_{\mathrm{eff}})$. Such an analysis could provide the first ever measurement of $f{\sigma }_8(z_{\mathrm{eff}})$ at redshift $z_{\mathrm{eff}}>2$. By combining this with the quasar auto-correlation in a joint analysis of the three high-redshift two-point correlation functions, we show that DESI could be able to measure $f{\sigma }_8(z_{\mathrm{eff}}\simeq 2.3)$ with a precision of $5-12\%$, depending on the smallest scale fitted.

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