Laguerre reconstruction of the correlation function on Baryon Acoustic Oscillation scales

The baryon acoustic oscillation feature can be used as a standard cosmological ruler. In practice, for sub-percent level accuracy on the distance scale, it must be standardized. The physical reason why is understood, so we use this to develop an algorithm which improves the estimated scale. The algorithm exploits the fact that, over the range of scales where the initial correlation function is well-fit by a polynomial, the leading order effects which distort the length of the ruler can be accounted for analytically. Tests of the method in numerical simulations show that it provides simple and fast reconstruction of the full shape of the BAO feature, as well as sub-percent determination of the linear point in the correlation function of biased tracers with minimal assumptions about the underlying cosmological model or the nature of the observed tracers. Our results also suggest that, for least squares estimators of the correlation function, half-integer generalized Laguerre functions are a particularly useful choice.