Model selection with the Pantheon+ Type Ia SN sample

TL;DR

This study compares the standard $ ext{Lambda}$CDM model and the $R_{ m h}=ct$ universe using Pantheon+ Type Ia supernova data, finding that the latter better satisfies energy conditions and is statistically favored.

Contribution

It introduces a model-independent method to test energy conditions with supernova data and compares $ ext{Lambda}$CDM and $R_{ m h}=ct$ using this approach.

Findings

$ ext{Lambda}$CDM violates the strong energy condition at $z o 0$ to 2.

$R_{ m h}=ct$ satisfies all four energy conditions.

$R_{ m h}=ct$ is favored over $ ext{Lambda}$CDM with 89.5\% likelihood.

Abstract

Recent discoveries, e.g., by JWST and DESI, have elevated the level of tension with inflationary $\Lambda$CDM. 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. In this Letter, we use a recently compiled Type Ia supernova sample to examine whether $\Lambda$CDM violates the energy conditions in the local Universe, and carry out model selection with its principal competitor, the $R_{\rm h}=ct$ universe. We derive model-independent constraints on the distance modulus based on the energy conditions and compare these with the Hubble diagram predicted by both $\Lambda$CDM and $R_{\rm h}=ct$, using the Pantheon+ Type Ia supernova catalog. We find that $\Lambda$CDM violates the strong energy condition over the redshift range $z \subset (0, 2)$, whereas $R_{\rm h}=ct$ satisfies all four energy constraints. At the same time, $R_{\rm h}=ct$ is favored by these data over $\Lambda$CDM with a likelihood of $\sim 89.5\%$ versus $\sim 10.5\%$. The $R_{\rm h}=ct$ model without inflation is strongly favored by the Type Ia supernova data over the currrent standard model, while simultaneously adhering to the general relativistic energy conditions at both high and low redshifts.