Neutrino Mass Constraints from Reconstructing the Large-scale Structure: Systematic Uncertainty

We examine the possibility of applying the baryonic acoustic oscillation reconstruction method to improve the neutrino mass sigma m (nu) constraint. Thanks to the Gaussianization of the process, we demonstrate that the reconstruction algorithm could improve the measurement accuracy by roughly a factor of two. On the other hand, the reconstruction process itself becomes a source of systematic error. While the algorithm is supposed to produce the displacement field from a density distribution, various approximations cause the reconstructed output to deviate on intermediate scales. Nevertheless, it is still possible to benefit from this Gaussianized field, given that we can carefully calibrate the "transfer function" between the reconstruction output and theoretical displacement divergence from simulations. The limitation of this approach is then set by the numerical stability of this transfer function. With an ensemble of simulations, we show that such systematic error could become comparable to statistical uncertainties for a DESI-like survey and be safely neglected for other less ambitious surveys.