Supernova Magnitude Evolution and PAge Approximation

The evidence of environmental dependence of Type Ia supernova luminosity has inspired recent discussion about whether the late-universe cosmic acceleration is still supported by supernova data. We adopt the $\Delta\mathrm{HR}/\Delta\mathrm{age}$ parameter, which describes the dependence of supernova absolute magnitude on the age of supernova progenitor, as an additional nuisance parameter. Using the Pantheon supernova data, a lower bound $\ge 12\,\mathrm{Gyr}$ on the cosmic age, and a Gaussian prior $H_0 = 70\pm 2\,\mathrm{km\,s^{-1}Mpc^{-1}}$ on the Hubble constant, we reconstruct the cosmic expansion history. Within the flat $\Lambda$ cold dark matter ($\Lambda$CDM) framework, we still find a $5.6\sigma$ detection of cosmic acceleration. This is because a matter dominated decelerating universe would be too young to accommodate observed old stars with age $\gtrsim 12\,\mathrm{Gyr}$. A decelerating but non-flat universe is marginally consistent with the data, however, only in the presence of a negative spatial curvature $\sim$ two orders of magnitude beyond the current constraint from cosmic microwave background data. Finally, we propose a more general Parameterization based on the cosmic Age (PAge), which is {\it not} directly tied to the dark energy concept and hence is ideal for a null test of the cosmic acceleration. We find that, for a magnitude evolution rate $\Delta\mathrm{HR}/\Delta\mathrm{age} \lesssim 0.3\,\mathrm{mag}/5.3\,\mathrm{Gyr}$ (Kang et al. 2020), a spatially flat and decelerating PAge universe is fully consistent with the supernova data and the cosmic age bound, and has no tension with the geometric constraint from the observed CMB acoustic angular scales.