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-5łog(z(1+z)) and z, implying that their magnitude--redshift relation can be parametrised with just two parameters: an intercept z(1+z)10^ and a slope b. This relation corresponds to the luminosity distance d_L(z)=c,H_0^ -1 bz/5 and is valid up to at least z It outperforms the ΛCDM and flat wCDM 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 and b.