The negative BAO shift in the Ly$\alpha$ forest from cosmological simulations

We present the first measurement of the Ly$\alpha$ forest BAO shift parameter from cosmological simulations. In particular, we generate a suite of $1000$ accurate effective field-level bias-based Ly$\alpha$ forest simulations of volume $V=(1 \, h^{-1} \, {\rm Gpc})^3$ at $z=2$, both in real and redshift space, calibrated upon two fixed-and-paired cosmological hydrodynamic simulations. To measure the BAO, we stack the three-dimensional power spectra of the $1000$ different realizations, compute the average, and use a model accounting for a proper smooth-peak component decomposition of the power spectrum, to fit it via an efficient Markov Chain Monte Carlo scheme estimating the covariance matrices directly from the simulations. We report the BAO shift parameters to be $\alpha=0.9969^{+0.0014}_{-0.0014}$ and $\alpha=0.9905^{+0.0027}_{-0.0027}$ in real and redshift space, respectively. We also measure the bias $b_{\rm lya}$ and the BAO broadening parameter $\Sigma_{\rm nl}$, finding $b_{\rm lya}=-0.1786^{+0.0001}_{-0.0001}$ and $\Sigma_{\rm nl}=3.87^{+0.20}_{-0.20}$ in real space, and $b_{\rm lya}=-0.073^{+0.005}_{-0.004}$ and $\Sigma_{\rm nl}=6.55^{+0.23}_{-0.22}$ in redshift space. Moreover, we measure the linear Kaiser factor $\beta_{\rm lya}=1.39^{+0.24}_{-0.18}$ from the isotropic redshift space fit. Overall, we find evidence for a negative shift of the BAO peak at the $\sim 2.2\sigma$ and $\sim 3.5\sigma$ level in real and redshift space, respectively. This work sets new important theoretical constraints on the Ly$\alpha$ forest BAO scale and offers a potential solution to the tension emerging from previous observational analysis, in light of ongoing and upcoming Ly$\alpha$ forest spectroscopic surveys, such as DESI, PFS, and WEAVE-QSO.