On the bin sensitivity of the transverse BAO

Abstract The BAO characteristic scale is a useful tool for understanding the evolution of the universe, especially the influence of dark energy on this evolution. In this work, we study the projection effect in transverse BAO, namely the mixing of BAO signals from different epochs caused by z c uncertainty within a chosen bin. We focus our forecast on two surveys of interest: the Square Kilometre Array (SKA) HI galaxy redshift survey and the Dark Energy Spectroscopic Instrument (DESI)'s final Luminous Red Galaxy (LRG) sample. We test the sensitivity in finding the transverse BAO depending of three bin configurations: a Gaussian, a top-hat and an intermediate of them semi-Gaussian. We also analyse the precision the bin widths σ z from smaller to wider bins 0.01 < σ z < 0.1. In order to correct these deviations, we propose a correction based on adjacent redshift to z c , this would provide a statistical correction instead of only relying on fiducial cosmology. Finally, we conclude that despite the higher shot-noise than the top-hat bin separation, the semi-Gaussian bin is the most accurate case to find the BAO signal for most bin widths ( σ z < 0.04) we tested. For a SKA-like survey, Gaussian binning yields the weakest parameter constraints among the three options. In contrast, for a DESI-like survey, this trend reverses: the semi-Gaussian scheme provides the tightest constraints, but only when σ z < 0.04, while for larger σ z values the Gaussian and top-hat binnings deliver similarly strong constraints. For a real data pipeline, one must choose which approach is best: well constrained cosmological parameters, but less accurate BAO measurement; or well measured BAO peak/wiggles. In case one is interested in combining the BAO measurement with other cosmological probes, it might be more interesting to focus on the bin scheme that is statistically robust and with a sharp representation of the redshift of interest, which is the Semi-Gaussian case.