Small-scale structure and the Lyman-$α$ forest baryon acoustic oscillation feature

The baryon-acoustic oscillation (BAO) feature in the Lyman-$\alpha$ forest is one of the key probes of the cosmic expansion rate at redshifts z~2.5, well before dark energy is believed to have become dynamically significant. A key advantage of the BAO as a standard ruler is that it is a sharp feature and hence is more robust against broadband systematic effects than other cosmological probes. However, if the Lyman-$\alpha$ forest transmission is sensitive to the initial streaming velocity of the baryons relative to the dark matter, then the BAO peak position can be shifted. Here we investigate this sensitivity using a suite of hydrodynamic simulations of small regions of the intergalactic medium with a range of box sizes and physics assumptions; each simulation starts from initial conditions at the kinematic decoupling era (z~1059), undergoes a discrete change from neutral gas to ionized gas thermal evolution at reionization (z~8), and is finally processed into a Lyman-$\alpha$ forest transmitted flux cube. Streaming velocities suppress small-scale structure, leading to less violent relaxation after reionization. The changes in the gas distribution and temperature-density relation at low redshift are more subtle, due to the convergent temperature evolution in the ionized phase. The change in the BAO scale is estimated to be of the order of 0.12% at z=2.5; some of the major uncertainties and avenues for future improvement are discussed. The predicted streaming velocity shift would be a subdominant but not negligible effect (of order $0.26\sigma$) for the upcoming DESI Lyman-$\alpha$ forest survey, and exceeds the cosmic variance floor. It is hoped that this study will motivate additional theoretical work on the magnitude of the BAO shift, both in the Lyman-$\alpha$ forest and in other tracers of large-scale structure.

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