More accurate simulations with separate initial conditions for baryons and dark matter

We revisit techniques for performing cosmological simulations with both baryons and cold dark matter when each fluid has different initial conditions, as is the case at the end of the radiation era. Most simulations do not reproduce the linear prediction for the difference between the cold dark matter and baryon perturbations. We show that this is due to the common use of offset regular grids when setting up the particle initial conditions. The desired linear evolution can be obtained without any loss of simulation resolution by using a Lagrangian glass for the baryon particles. We further show that the difference between cold dark matter and baryons may affect predictions for the Lyman-$\alpha$ forest flux power spectrum at the $5\%$ level, potentially impacting current cosmological constraints.