BAO cosmology in non-spatially flat background geometry with application to BOSS and eBOSS

We study the impact of the assumption of a non-flat fiducial cosmology on the measurement, analysis and interpretation of BAO distance variables, along and across the line-of-sight. The assumption about cosmology enters in the choice of the base template, as well as on the transformation of tracer's redshifts into distances (the catalog cosmology): here we focus on the curvature assumption, separately and jointly, on both. We employ BOSS and eBOSS publicly available data and show that for the statistical precision of this data set, distance measures and thus cosmological inference are robust to assumptions about curvature both of the template and the catalog. Thus the usual assumptions of flat fiducial cosmologies (but also assumptions of non-flat cosmologies) do not produce any detectable systematic effects. For forthcoming large-volume surveys, however, small but appreciable residual systematic shifts can be generated which may require some care. These are mostly driven by the choice of catalog cosmology if it is significantly different from true cosmology. In particular, the catalog (and template) cosmology should be chosen, possibly iteratively, in such a way that the recovered BAO scaling variables are sufficiently close to unity. At this level of precision, however, other previously overlooked effects become relevant, such as a mismatch between the sound horizon as seen in the BAO and the actual sound horizon in the early Universe. If unaccounted for, such effect may be misinterpreted as cosmological and thus bias the curvature (and cosmology) constraints.