Evolution of the LsSFR bias, −ψ(z) × Δ_Y, with redshift, as predicted by Eq (7). The blue band shows the expected redshift evolution of −ψ(z) × Δ_Y when accounting for uncertainties on ϕ. The result of using the ψ(z) parametrization in Rigault et al. (2013) is shown as a blue dash line for comparison (see also Childress et al. 2014). To quantify the impact of the LsSFR bias, we simulate data following the expected SN rate and data quality of ZTF, LSST and EUCLID/DESIRE (see text). The expected numbers of SNe Ia are shown above the main plot on a logarithmic scale, color coded by sample. The expected binned uncertainties on the measurements of −ψ(z) × Δ_Y are shown in the main plot, following the same color code. Randomly drawn MCMC realizations of the fitted magnitude difference between a flat w₀ w_aCMD and a flat ΛCDM are shown as a grey band. The black line is the best fit value. The extracted w₀, w_a posterior distribution is displayed in the inset plot. This figure illustrates that the LsSFR bias would be mistakenly attributed to the key properties of dark energy that future surveys hope to measure.