Direct cosmological inference from three-dimensional correlations of the Lyman-$\alpha$ forest

TL;DR

This paper demonstrates that fitting the full shape of the Lyman-alpha correlation functions, instead of just the BAO peak, significantly improves constraints on cosmological parameters like matter density and growth rate.

Contribution

It introduces a direct fitting method to extract all physical information from Lyman-alpha correlation functions, surpassing traditional BAO-only analyses.

Findings

3.5% constraint on matter density, three to four times better than BAO alone

10% constraint on growth rate $f \sigma_8$

3-4% constraint on spectral index $n_s$

Abstract

When performing cosmological inference, standard analyses of the Lyman-$\alpha$ (Ly$\alpha$) three-dimensional correlation functions only consider the information carried by the distinct peak produced by baryon acoustic oscillations (BAO). In this work, we address whether this compression is sufficient to capture all the relevant cosmological information carried by these functions. We do this by performing a direct fit to the full shape, including all physical scales without compression, of synthetic Ly$\alpha$ auto-correlation functions and cross-correlations with quasars at effective redshift $z_{\rm{eff}}=2.3$, assuming a DESI-like survey, and providing a comparison to the classic method applied to the same dataset. Our approach leads to a $3.5\%$ constraint on the matter density $\Omega_{\rm{M}}$, which is about three to four times better than what BAO alone can probe. The growth term $f \sigma_{8} (z_{\rm{eff}})$ is constrained to the $10\%$ level, and the spectral index $n_{\rm{s}}$ to $\sim 3-4\%$. We demonstrate that the extra information resulting from our `direct fit' approach, except for the $n_{\rm{s}}$ constraint, can be traced back to the Alcock-Paczy\'nski effect and redshift space distortion information.