Probing the matter-dominated expansion with multi-redshift Lyman-$\alpha$ BAO from DESI DR2

Abstract

We present a multi-redshift Baryon Acoustic Oscillations (BAO) analysis of the DESI Data Release 2 (DR2) Lyman-$\alpha$ (Ly$\alpha$) forest, splitting the forest auto-correlation and its cross-correlation with quasars into three redshift bins. We obtain BAO measurements at effective redshifts $z_{\rm eff} = 2.13$, $2.40$, and $2.81$ with $\sim2.0$--$2.5\%$ precision per bin in the radial and transverse directions, corresponding to $\sim1.1$--$1.2\%$ precision for the isotropic BAO measurement. Using the same data products and modeling framework as the DESI DR2 Ly$\alpha$ BAO analysis, we validate the pipeline on $400$ synthetic datasets and find unbiased BAO recovery with well-calibrated uncertainties. The measurements show an increase in the isotropic dilation parameter $D_V/r_d$ from $30.26\pm0.39$ to $32.22\pm0.47$ and in the Alcock-Paczy\'nski parameter $D_M/D_H$ from $3.96\pm0.15$ to $5.63^{+0.22}_{-0.24}$. The Hubble distance $D_H/r_d$ decreases from $9.40\pm0.20$ to $7.22\pm0.17$, providing a direct measurement of the expansion history consistent with $\Lambda$CDM and the expected matter-dominated scaling, with $H(z)\propto(1+z)^n$ giving $n=1.34\pm0.16$. The redshift split also provides a self-consistent measurement of clustering evolution: the Ly$\alpha$ forest bias evolves as $(1+z)^\gamma$ with $\gamma_\alpha=3.05\pm0.16$, the RSD parameter has a redshift evolution described by $\gamma_\beta=-0.97\pm0.26$, and the quasar bias evolves with $\gamma_Q=1.56\pm0.23$, consistent with independent quasar clustering measurements. Combining these three-bin BAO measurements with DESI DR2 galaxy and quasar BAO measurements yields cosmological constraints consistent with the single-bin Ly$\alpha$ BAO analysis in flat $\Lambda$CDM and $w_0w_a$CDM and improves curvature constraints by $\sim12\%$ in $\Lambda$CDM$+\Omega_\mathrm{K}$.