Comparison of cosmological constraints from BAO measurements and our implementation of AP test in ALTAIR. The grey and green lines denote the 1σ confidence region, centred on the fiducial cosmological parameters, obtained from our AP test and BAO constraints from SDSS-III (DR 12; Alam et al. 2017), respectively. The BAO constraints have not been combined with Planck CMB measurements. This demonstrates the potentially unprecedented constraining power of our AP test compared to standard BAO analyses, as discussed in Sect. 2, with the inset focusing on the ALTAIR constraints where the fiducial cosmology is depicted in dashed lines. This error forecast is validated on a simulated analysis (cf. Fig. 6).