A new magnitude–redshift relation based on Type Ia supernovae

We present a new empirical relation between the standardised magnitude ( m ) of Type Ia supernovae (SNe Ia) and redshift ( z ). Using the Pantheon+ sample and the Dark Energy Survey (DES) five-year sample (DES-SN5YR), we find a negative linear correlation between m − 5log( z (1 + z )) and z , implying that their magnitude–redshift relation can be parametrised with just two parameters: an intercept ℳ and a slope b . This relation corresponds to the luminosity distance d L ( z ) = c H 0 −1 z (1 + z )10 bz /5 and is valid up to at least z ≃ 1.1. It outperforms the ΛCDM and flat w CDM models and the (2,1) Padé approximant for d L ( z ), and performs comparably to the flat ΛCDM model and the (2,1) Padé( j 0 = 1) model of Hu et al. Furthermore, the relation is relatively stable in the absence of low- z SNe, making it suitable for fitting Hubble diagrams of SNe Ia without adding a low- z sample. In deep fields, assuming that the large-scale density is independent of the comoving radial coordinate, b ∝ q 0 + 1. We fitted the empirical relation to Hubble diagrams of eight deep-field regions and find no evidence for anisotropy. The inferred q 0 values, ranging from −0.6 to −0.4, are consistent within 1.6 σ and significantly lower than zero, indicating statistically consistent cosmic acceleration across all eight regions. We applied the empirical relation to the DES-Dovekie and Amalgame SN samples and find b values consistent with those from DES-SN5YR and Pantheon+. Finally, using the empirical relation in the hemispheric comparison method applied to Pantheon+ up to z = 1.1, we find no evidence for anisotropies in ℳ and b .