Letter to the Editor

Model selection with the Pantheon+ Type Ia supernova sample

¹ Department of Physics, The University of Arizona Tucson Arizona 85721, USA
² Department of Physics, The Applied Math Program, and Department of Astronomy, The University of Arizona Tucson Arizona 85721, USA
³ Purple Mountain Observatory, Chinese Academy of Sciences Nanjing 210023, China

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 15 January 2026
Accepted: 4 February 2026

Abstract

Context. Recent discoveries, for example by JWST and DESI, have elevated the level of tension with inflationary Λ cold dark matter (ΛCDM). For example, the empirical evidence now suggests that the standard model violates at least one of the energy conditions from general relativity, which were designed to ensure that systems have positive energy, attractive gravity, and non-superluminal energy flows.

Aims. We used a recently compiled Type Ia supernova sample to examine whether ΛCDM violates the energy conditions in the local Universe, and carried out model selection with its principal competitor, the R_h = ct universe.

Methods. We derived model-independent constraints on the distance modulus based on the energy conditions and compared them with the Hubble diagram predicted by both ΛCDM and R_h = ct, using the Pantheon+ Type Ia supernova catalogue.

Results. We find that ΛCDM violates the strong energy condition over the redshift range z ⊂ (0, 2), whereas R_h = ct satisfies all four energy constraints. At the same time, R_h = ct is favoured by these data over ΛCDM with a likelihood of ∼89.8% versus ∼10.2%.

Conclusions. The R_h = ct model without inflation is strongly favoured by the Type Ia supernova data over the current standard model, while simultaneously adhering to the general relativistic energy conditions at both high and low redshifts.