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The tight-coupling approximation for baryon acoustic oscillations

The tight-coupling approximation (TCA) used to describe the early dynamics of the baryons-photons system is systematically built to higher orders in the inverse of the interaction rate. This expansion can be either used to grasp the physical effects by deriving simple analytic solutions or to obtain a form of the system which is stable numerically at early times. In linear cosmological perturbations, we estimate numerically its precision, and we discuss the implications for the baryons acoustic oscillations. The TCA can be extended to the second order cosmological perturbations, and in particular we recover that vorticity is not generated at lowest order of this expansion.