Model selection with the Pantheon+ Type Ia SN sample

TL;DR

This work tests whether the standard inflationary $Λ$CDM cosmology violates general-relativistic energy conditions by leveraging the Pantheon+ Type Ia SN sample. By deriving model-independent SEC-based bounds on the distance modulus and comparing against predictions from $Λ$CDM and the $R_{h}=ct$ cosmology, the authors show that $Λ$CDM violates the Strong Energy Condition over $z\in(0,2)$ while $R_{h}=ct$ satisfies all energy conditions. A Bayesian-like model comparison using the Bayes Information Criterion favors $R_{h}=ct$ with approximately $89.8\%$ support over $Λ$CDM’s $\sim10.2\%$, suggesting the data prefer a linear expansion without inflation. The results reinforce energy conditions as a guiding constraint and imply that a cosmological model with $R_{h}=ct$ provides a better low-redshift fit to Type Ia SN data than the current standard model. The study thereby contributes to the broader discussion on the nature of dark energy and the viability of alternative FLRW cosmologies. All mathematical notation is presented with $...$ delimiters.

Abstract

Recent discoveries, e.g., by JWST and DESI, have elevated the level of tension with inflationary $Λ$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 $Λ$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 $Λ$CDM and $R_{\rm h}=ct$, using the Pantheon+ Type Ia supernova catalog. We find that $Λ$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 $Λ$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.

Figures (4)

• Figure 1: Distance modulus for the Type Ia SNe in the $R_{\rm h}=ct$ model. The predicted (dashed) curve is coincident with the SEC limit (blue curve), as highlighted in the plot (Figure \ref{['f4']}) without the data.
• Figure 2: 1D probability distributions and 2D regions with the $1 - 2\sigma$ contours for the parameters $M_B$, $\alpha$, and $\beta$ in $\Lambda$CDM (blue) and in $R_{\rm h}=ct$ (red), corresponding to the fits in Figures \ref{['f1']} and \ref{['f3']}. Note that not all best fit values in both models are the same.
• Figure 3: Distance modulus for the Type Ia SNe in flat-$\Lambda$CDM. The model prediction (dashed curve) violates the SEC limit (blue curve) in the redshift range $z \subset (0.125, 2)$, as shown more clearly without the data in Figure \ref{['f4']}.
• Figure 4: The optimized theoretical curves from Figures \ref{['f1']} and \ref{['f3']}, together with the SEC upper bound (blue), showing full compliance by $R_{\rm h}=ct$ (dotted) and a violation by flat-$\Lambda$CDM (dashed).