DESI DR2 Results IV: Alcock-Paczy'nski Measurements from the Lyman Alpha Forest and Cosmological Constraints
Published in arXiv e-prints, 2026
DESI Collaboration, A. Adame, J. Aguilar, S. Ahlen, O. Alves, A. Anand, et al. "DESI DR2 Results IV: Alcock-Paczy'nski Measurements from the Lyman Alpha Forest and Cosmological Constraints." arXiv e-prints, 2026.
Abstract
We present Alcock-Paczyński (AP) measurements from the full shape of Lyman-$α$ (Ly$α$) forest correlation functions measured from the second data release (DR2) of the Dark Energy Spectroscopic Instrument (DESI). Our measurements include information from the Ly$α$ forest auto-correlation and its cross-correlation with quasars. We constrain the AP effect with $1%$ precision at an effective redshift $z_mathrmeff=2.33$, which is twice as tight as the Baryon Acoustic Oscillation (BAO) constraint from the same data. When using the joint Ly$α$ AP and BAO results, we measure the ratios $D_textH(z_mathrmeff)/r_textd=8.600 pm 0.066$ and $D_textM(z_mathrmeff)/r_textd=39.32 pm 0.33$, where $D_textM$ is the transverse comoving distance, $D_textH$ is the Hubble distance, and $r_textd$ is the sound horizon at the drag epoch. Assuming $Λ$CDM, Ly$α$ forest measurements combined with a nucleosynthesis prior produce a constraint on the Hubble constant $H_0=66.5pm1.3,mathrmkm,s^-1,Mpc^-1$. The Ly$α$ AP result corresponds to a matter fraction constraint $Ω_textm=0.325pm0.018$ in $Λ$CDM, which is $1.4σ$ higher than DESI BAO. This impacts the DESI results relative to the Cosmic Microwave Background (CMB), slightly reducing their discrepancy from $2.4σ$ to $2.2σ$. We present updated constraints on extended models using the joint DESI DR2 BAO and Ly$α$ forest full shape data, together with external data sets. When considering a time-evolving dark energy equation of state parametrized by $w_0$ and $w_a$, we find it is preferred over $Λ$CDM at $2.7σ$ for the combination of DESI and CMB data, and at $3.2σ$ when also including supernovae. With the new Ly$α$ AP measurement, DESI provides its most precise anchor for the expansion history at $z > 1$ in the matter-dominated Universe.