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

TL;DR

This paper introduces a new full-shape fitting method for the 3D correlation function of the Lyman-alpha forest to enhance cosmological measurements beyond traditional BAO analysis, particularly at high redshift.

Contribution

It proposes a novel full-shape analysis technique for the Lyman-alpha forest, improving constraints on cosmological parameters and measuring the growth rate at high redshift.

Findings

Expected 0.9% precision on H(z)r_d and D_M(z)/r_d from DESI data.

Potential to measure fσ_8(z) at z>2 for the first time.

Joint analysis could achieve 5-12% precision on fσ_8 at z~2.3.

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 $\sim0.9\%$ 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 $z_\mathrm{eff}\simeq2.3$. By fitting the AP parameter from the full shape of the two correlations, we show that we can obtain a precision of $\sim0.5-0.6\%$ 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 $8\;h^{-1}$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 $f\sigma_8(z_\mathrm{eff}\simeq2.3)$ with a precision of $5-12\%$, depending on the smallest scale fitted.