A new magnitude–redshift relation based on Type Ia supernovae

¹ Pontificia Universidad Católica de Chile, Vicuña Mackenna, 4860 Macul, Santiago, Chile
² Instituto Milenio de Astrofísica (MAS), Nuncio Monseñor Sótero Sanz 100, Of. 104, Santiago, Chile

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Received: 13 January 2026
Accepted: 2 March 2026

Abstract

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 H₀⁻¹z(1 + z)10^bz/5 and is valid up to at least z ≃ 1.1. 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(j₀ = 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 ∝ q₀ + 1. We fitted the empirical relation to Hubble diagrams of eight deep-field regions and find no evidence for anisotropy. The inferred q₀ values, ranging from −0.6 to −0.4, are consistent within 1.6σ 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.