Correcting cosmological parameter biases for all redshift surveys induced by estimating and reweighting redshift distributions

Photometric redshift uncertainties are a major source of systematic error for ongoing and future photometric surveys. We study different sources of redshift error caused by choosing a suboptimal redshift histogram bin width and propose methods to resolve them. The selection of a too large bin width is shown to oversmooth small scale structure of the radial distribution of galaxies. This systematic error can significantly shift cosmological parameter constraints by up to $6 \, \sigma$ for the dark energy equation of state parameter $w$. Careful selection of bin width can reduce this systematic by a factor of up to 6 as compared with commonly used current binning approaches. We further discuss a generalised resampling method that can correct systematic and statistical errors in cosmological parameter constraints caused by uncertainties in the redshift distribution. This can be achieved without any prior assumptions about the shape of the distribution or the form of the redshift error. Our methodology allows photometric surveys to obtain unbiased cosmological parameter constraints using a minimum number of spectroscopic calibration data. For a DES-like galaxy clustering forecast we obtain unbiased results with respect to errors caused by suboptimal histogram bin width selection, using only 5k representative spectroscopic calibration objects per tomographic redshift bin.